Van Der Vorst Research Articles

Influences, practices and opportunities for environmental supply chain management in Nova Scotia SMEs

Executives are increasingly paying attention to the importance of supply chain management [Lambert DM, Cooper MC. Issues in supply chain management. Industrial Marketing Management 2000;29(1):65–83; Hagelaar GJLF, van der Vorst JGAJ. Environmental supply chain management: using life cycle assessment to structure supply chains. International Food and Agribusiness Management Review 2002;4:399–412]. The management of the supply chain can be a central aspect of a company's competitive advantage [Preuss L. Rhetoric and reality of corporate greening: a view from the supply chain management function. Business Strategy and the Environment 2005;14:123–139]. SCM also offers considerable opportunities to reduce a company's environmental impact. The supply chains of three small and medium enterprises (SMEs) operating in the Burnside Industrial Park in Nova Scotia, Canada were investigated to explore the opportunities to improve environmental performance of SMEs linked in supply chains. This study confirmed that time and, to a lesser degree, financial resources to address solid waste and energy issues are the greatest limiting factors. Small suppliers, and even to a certain degree medium-sized enterprises, have difficulties in allocating resources to initiatives that are not viewed as directly related to their core function, namely manufacturing the product or providing the service. This study clearly demonstrated that opportunities exist to reduce greenhouse gas emissions and solid waste. Although, the benefits that would be gained from the implementation of any of the individual actions in the supply chains explored in this study are individually small, the cumulative benefits that could be achieved among supply chains and within industrial parks are substantial, given the number of small- and medium-sized enterprises.

An improved parallel hybrid bi-conjugate gradient method suitable for distributed parallel computing

An improved parallel hybrid bi-conjugate gradient method (IBiCGSTAB(2) method, in brief) for solving large sparse linear systems with nonsymmetric coefficient matrices is proposed for distributed parallel environments. The method reduces five global synchronization points to two by reconstructing the BiCGSTAB(2) method in [G.L.G. Sleijpen, H.A. van der Vorst, Hybrid bi-conjugate gradient methods for CFD problems, in: M. Hafez, K. Oshima (Eds.), Computational Fluid Dynamics Review 1995, John Wiley & Sons Ltd, Chichester, 1995, pp. 457–476] and the communication time required for the inner product can be efficiently overlapped with useful computation. The cost is only slightly increased computation time, which can be ignored, compared with the reduction of communication time. Performance and isoefficiency analysis shows that the IBiCGSTAB(2) method has better parallelism and scalability than the BiCGSTAB(2) method. Numerical experiments show that the scalability can be improved by a factor greater than 2.5 and the improvement in parallel communication performance approaches 60%.

Special Issue on Tensor Decompositions and Applications

This issue of SIAM Journal on Matrix Analysis and Applications was motivated by the Workshop on Tensor Decompositions and Applications, held in Luminy, France from August 29 to September 2, 2005. The issue was announced through both the SIMAX and the workshop web sites. Though decompositions of higher-order tensors have been around for many years, the door is now opening on greater mathematical understanding and new applications. Tensor decompositions have been applied by researchers in psychometrics and chemometrics since the seventies. More recently, tensors have found their way to signal processing via the use of high-order statistics, joint matrix techniques, and applications in telecommunications. Other applications include complexity theory, (blind) system identification, biomedical engineering, numerical analysis, and data mining, among others. This volume contains 15 papers that together form a nice cross-section of current research on tensor decompositions. The papers present new algorithms, basic algebraic results including the introduction of new decompositions, and applications in signal processing, scientific computing, and large-scale problems. Many thanks are due to all the authors for their valuable contributions. We would also like to thank Henk van der Vorst, Mitch Chernoff, and the SIAM staff for their support. Since the initial submission of the papers, two of the authors have passed away. Richard Harshman and Gene Golub were both authorities in their field.

Drugs and the kidney: more than a question of dose

Drugs and the kidney: more than a question of dose

Targeted excited state algorithms

To overcome the limitations of the traditional state-averaging approaches in excited state calculations, where one solves and represents all states between the ground state and excited state of interest, we have investigated a number of new excited state algorithms. Building on the work of van der Vorst and Sleijpen [SIAM J. Matrix Anal. Appl. 17, 401 (1996)], we have implemented harmonic Davidson and state-averaged harmonic Davidson algorithms within the context of the density matrix renormalization group (DMRG). We have assessed their accuracy and stability of convergence in complete-active-space DMRG calculations on the low-lying excited states in the acenes ranging from naphthalene to pentacene. We find that both algorithms offer increased accuracy over the traditional state-averaged Davidson approach, and, in particular, the state-averaged harmonic Davidson algorithm offers an optimal combination of accuracy and stability in convergence.

PHOENIX: MHD spectral code for rotating laboratory and gravitating astrophysical plasmas

The new PHOENIX code is discussed together with a sample of many new results that are obtained concerning magnetohydrodynamic (MHD) spectra of axisymmetric plasmas where flow and gravity are consistently taken into account. PHOENIX, developed from the CASTOR code [W. Kerner, J.P. Goedbloed, G.T.A. Huysmans, S. Poedts, E. Schwarz, J. Comput. Phys. 142 (1998) 271], incorporates purely toroidal, or both toroidal and poloidal flow and external gravitational fields to compute the entire ideal or resistive MHD spectrum for general tokamak or accretion disk configurations. These equilibria are computed by means of FINESSE [A.J.C. Beliën, M.A. Botchev, J.P. Goedbloed, B. van der Holst, R. Keppens, J. Comp. Physics 182 (2002) 91], which discriminates between the different elliptic flow regimes that may occur. PHOENIX makes use of a finite element method in combination with a spectral method for the discretization. This leads to a large generalized eigenvalue problem, which is solved by means of Jacobi–Davidson algorithm [G.L.G. Sleijpen, H.A. van der Vorst, SIAM J. Matrix Anal. Appl. 17 (1996) 401]. PHOENIX is compared with CASTOR, PEST-1 and ERATO for an internal mode of Soloviev equilibria. Furthermore, the resistive internal kink mode has been computed to demonstrate that the code can accurately handle small values for the resistivity. A new reference test case for a Soloviev-like equilibrium with toroidal flow shows that, on a particular unstable mode, the flow has a quantifiable stabilizing effect regardless of the direction of the flow. PHOENIX reproduces the Toroidal Flow induced Alfvén Eigenmode (TFAE, [B. van der Holst, A.J.C. Beliën, J.P. Goedbloed, Phys. Rev. Lett. 84 (2000) 2865]) where finite resistivity in combination with equilibrium flow effects causes resonant damping. Localized ideal gap modes are presented for tokamak plasmas with toroidal and poloidal flow. Finally, we demonstrate the ability to spectrally diagnose magnetized accretion disk equilibria where gravity acts together with either purely toroidal flow or both toroidal and poloidal flow. These cases show that the MHD continua can be unstable or overstable due to the presence of a gravitational field together with equilibrium flow-driven dynamics [J.P. Goedbloed, A.J.C. Beliën, B. van der Holst, R. Keppens, Phys. Plasmas 11 (2004) 28].

Integral resource management by exergy analysis for the selection of a separation process in the pharmaceutical industry

Download options Please wait... Article information DOI https://doi.org/10.1039/B617505H Article type Paper Submitted 30 Nov 2006 Accepted 01 Mar 2007 First published 20 Mar 2007 Download Citation Green Chem., 2007,9, 785-791 BibTex EndNote MEDLINE ProCite ReferenceManager RefWorks RIS Permissions Request permissions Integral resource management by exergy analysis for the selection of a separation process in the pharmaceutical industry J. Dewulf, G. Van der Vorst, W. Aelterman, B. De Witte, H. Vanbaelen and H. Van Langenhove, Green Chem., 2007, 9, 785 DOI: 10.1039/B617505H To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page. Read more about how to correctly acknowledge RSC content. Social activity Tweet Share Search articles by author J. Dewulf G. Van der Vorst W. Aelterman B. De Witte H. Vanbaelen H. Van Langenhove

Pharmacotherapy during neonatal extracorporeal membrane oxygenation: toward an evidence-based approach

Van der Vorst and coworkers recently illustrated the large variability in furosemide regimens used in their unit. This finding at least suggests that we need more data on the pharmacokinetics and pharmacodynamics of this drug in neonates during treatment with extracorporeal membrane oxygenation, in order to ensure quality of care and safety, and to promote evidence-based prescription. The implementation of population pharmacokinetic models can further increase both the feasibility of such studies and the relevance of the results generated.

Copper Mountain Special Issue on Iterative Methods

The 9th Copper Mountain Conference on Iterative Methods was held April 2–7, 2006, in Copper Mountain, Colorado. The conference is organized by Front Range Scientific Computations, Inc., with co-organizers the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory, and the University of Maryland. Traditionally, the SIAM Journal on Scientific Computing (SISC) hosts a special issue on iterative methods that is open to the public and is announced well in advance through both the SISC and the Copper Mountain Conference web sites. I would like to thank the current members of the program committee for their service as guest editorial board. The committee members are Xiao-Chuan Cai, University of Colorado; Iain Duff, RAL and CERFACS; Roland Freund, University of California, Davis; Kirk Jordan, IBM, Watson Research Center; Tim Kelley, North Carolina State University; David Keyes, Columbia University; Tom Manteuffel, University of Colorado; Steve McCormick, University of Colorado; David Silvester, University of Manchester; Ray Tuminaro, Sandia National Laboratory; Henk van der Vorst, University of Utrecht; Homer Walker, Worcester Polytechnic Institute; Carol Woodward, Lawrence Livermore National Laboratory; Irad Yavneh, Technion. The committee is chaired by Howard Elman (University of Maryland) and myself. This issue contains 21 papers that largely reflect the topics presented at the conference, including papers that were part of the student papers competition. More specifically, we have papers covering the more traditional numerical linear algebra topic of preconditioning, including preconditioners for nonsymmetric problems in GMRES, radial basis function interpolation via preconditioned Krylov iterations, preconditioned eigensolvers, graph-based algorithms for preconditioning, and strategies for constructing block preconditioners for systems of PDEs, as well as some emerging new topics, such as preconditioners for stochastic elliptic PDEs and linear systems arising in interior point optimization methods. Most of the papers deal with some aspects of iterative methods for systems of algebraic equations; however, a paper on iterative optimization procedures with application to image registration also found its place in the issue. The overwhelming majority of the papers deal with various aspects of (mostly algebraic) multigrid (or (A)MG), ranging from theory of geometric MG applied to nontraditional formulation of Stokes problems to investigation of a number of algorithmic issues in AMG (such as the construction of the interpolation operator, coarsening strategies including for nonsymmetric problems), as well as the construction of specialized AMG algorithms for Google PageRank-like problems and for problems arising from higher-order spectral elements discretizations. Many thanks are due to all authors for their valuable contributions. I would like also to thank the SIAM staff for their constant support and efforts to bring this issue to life. Finally, let me acknowledge the traditional support for the conference from the US Department of Energy, the National Science Foundation, IBM, Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratory.

Family factors and adolescents' alcohol use: A reply to Chassin and Handley (2006) and Fromme (2006).

In this reply, the authors address the comments of L. Chassin and E. D. Handley (2006) and of K. Fromme (2006) on the authors' article, Attachment, Parental Control, and Early Development of Alcohol Use: A Longitudinal Study (H. van der Vorst, R. C. M. E. Engels, W. Meeus, M. Dekovic, & A. Vermulst, 2006). Further, the authors elaborate on some topics in the area of parenting and substance use-for example, testing bidirectional associations between parenting and adolescents' substance use, the importance of measuring substance-specific socialization, and the relevance of using within-family designs and multi-informant data.

Perineural Infusion of Local Anesthetics

Perineural Infusion of Local Anesthetics

Special Section On Preconditioning Techniques

At the Third International Conference on Preconditioning Techniques for Large Sparse Matrix Problems in Scientific and Industrial Applications, held in Napa, California, on October 27--29, 2003, Henk A. van der Vorst, Editor-in-Chief of the SIAM Journal on Matrix Analysis and Applications (SIMAX), expressed an interest in publishing in SIMAX a collection of articles that would focus on current research on preconditioning techniques for matrix computation. This special section on preconditioning techniques is the result of subsequent discussions with SIAM and SIMAX. Manuscripts were solicited through various channels, particularly from the speakers at the third preconditioning conference. The term preconditioning generally refers to the additional step designed to improve the performance of a matrix algorithm, such as the rate of convergence of a Krylov method. Preconditioning arises in a variety of matrix computation. However, the papers in this special section provide a snapshot of the ongoing research activities on preconditioning techniques specifically for the solution of systems of linear equations. Multilevel and multigrid preconditioning techniques are the focus of the papers by Notay; de Sterk, Yang, and Heys; and Vassilevski and Zikatanov. Bank, Wan, and Qu have considered correction and interpolation techniques for improving the convergence of a multigrid method for solving convection-diffusion equations. Bridson and Greif have used a combination of multiple preconditioners in an attempt to improve the convergence of an iterative method. Giraud and Gratton have employed first-order perturbation theory to derive the first-order perturbations on the eigenvalues of matrices preconditioned by some forms of spectral preconditioners, and thereby obtained some insight into the design of such preconditioners. Lee, Raghavan, and Ng have investigated the problem of improving the quality of incomplete factorization through row and column reordering techniques. Some of papers are problem specific. The paper by Benzi and Ng considers preconditioning techniques for Toeplitz least squares problems, while that by Botchev and Golub focuses on preconditioning techniques for saddle point problems. Le Borne and Grasedyck have employed sparse hierarchical matrix approximations as preconditioners in iterative methods for solving convection-dominated elliptic partial differential equations. Bardsley and Nagy have investigated preconditioning strategies for solving ill-posed inverse problems arising from image analysis. The editor-in-chief of this special section would like to thank Henk A. van der Vorst for the encouragement, as well as Mitch Chernoff and his staff in the SIAM office for the advice and support in putting the special section together. Michele Benzi, Edmond Chow, Yousef Saad, Valeria Simoncini, and Wei-Pai Tang served as guest editors; their effort was much appreciated. Last but not the least, the editor-in-chief would like to thank all the authors for submitting their manuscripts to the special section, and all the anonymous referees for their help in reviewing the manuscripts.

Special Issue on Accurate Solution Of Eigenvalue Problems

The occasion for this special issue is the Sixth International Workshop on Accurate Solution of Eigenvalue Problems, which took place at The Pennsylvania State University from May 22-25, 2006. This special issue provides an outlet for papers from the workshop and recognizes advances in the numerical solution of eigenvalue and related problems. This is the second such special issue published in the SIAM Journal on Matrix Analysis and Applications; the first was published in number 4 of volume 28 in connection with the Fifth International Workshop on Accurate Solution of Eigenvalue Problems, which took place in Hagen, Germany, from June 29 to July 1, 2004. The twelve papers in the current issue are concerned with a variety of aspects that arise in the computation of eigenvalues and invariant subspaces: perturbation bounds and sensitivity, accuracy and convergence behavior of algorithms, exploitation of structure in matrices, and particular engineering applications. Thanks go to SIMAX Editor-in-Chief, Henk van der Vorst; guest editors Jesse Barlow, Froilan Dopico, and Zlatko Drmac, who put great effort into the careful and timely review of papers; and Mitch Chernoff, Cherie Trebisky, and other members of the SIAM staff who worked hard to publish this special issue.

Copper Mountain Special Issue on Iterative Methods

The biennial Copper Mountain Conference on Iterative Methods was held March 28-April 2, 2004, in Copper Mountain, Colorado. In addition to the traditional management services provided by Front Range Scientific Computations, Inc., Howard Elman (University of Maryland) and Panayot Vassilevski (Center for Applied Scientific Computing at LLNL) served as co-chairs representing the conference's new organizing institutions. The Conference gratefully acknowledges support from all three major national labs---Los Alamos, Lawrence Livermore, and Sandia---as well as support from the Department of Energy, IBM, and the National Science Foundation. Traditionally, the Copper Mountain Conference is organized in cooperation with the Society for Industrial and Applied Mathematics (SIAM). This special issue was open to the public and was advertised in advance on the web sites of both the SIAM Journal on Scientific Computing (SISC) and the Copper Mountain Conference. There were 35 manuscripts submitted; 15 found their place in this special issue. It is the guest editor-in-chief's opinion that these papers reflect state-of-the-art trends in iterative methods, among them parallel-block preconditioning, various improved versions of GMRES (block, relaxed, and flexible), approximate factorization preconditioners for saddle-point problems, and iterative methods exploiting deflation. But above all, this special issue clearly demonstrates the strong impact of multigrid/multilevel methods as the unique optimal-order iterative methods in various areas of applications. It also demonstrates the search for optimal-order methods or preconditioners on the basis of multilevel ideas in variety of nontraditional areas. I would like to thank the guest editorial board---Loyce Adams, Xiao-Chuan Cai, Iain Duff, Roland Freund, Anne Greenbaum, Tim Kelley, David Keyes, Tom Manteuffel, Steve McCormick, Ray Tuminaro, Henk van der Vorst, Olof Widlund, and Carol Woodward of the conference program committee---as well as Raymond Chan of the SISC editorial board and the many anonymous referees for their hard work to help meet the strict deadlines. I would also like to thank the SIAM staff for their constant support and efforts to bring this issue to life. Of course, this issue would not have been possible without the authors' contributions. Some of these submissions also appeared in the student paper competition, a unique event at the Copper Mountain conferences that has proven to be a very successful forum for presenting the latest results in the field. We have had increasingly strong participation from very talented recent Ph.D. holders and current Ph.D. students in this competition. We thank all the authors for their valuable contributions and hope that this special issue will stimulate further progress in this exciting area of research.

A finite integration method for conformal, structured-grid, electromagnetic simulation

We describe a numerical scheme for solving Maxwell’s equations in the frequency domain on a conformal, structured, non-orthogonal, multi-block mesh. By considering Maxwell’s equations in a volume parameterized by dimensionless curvilinear coordinates, we obtain a set of tensor equations that are a continuum analogue of common circuit equations, and that separate the metrical and metric-free parts of Maxwell’s equations and the material constitutive relations. We discretize these equations using a new formulation that treats the electric field and magnetic induction using simple basis-function representations to obtain a discrete form of Faraday’s law of induction, but that uses finite integral representations for the displacement current and magnetic field to obtain a discrete form of Ampere’s law, as in the finite integration technique [T. Weiland, A discretization method for the solution of Maxwell’s equations for six-component fields, Electron. Commun. (AE U) 31 (1977) 116; T. Weiland, Time domain electromagnetic field computation with finite difference methods, Int. J. Numer. Model: Electron. Netw. Dev. Field 9 (1996) 295–319]. We thereby derive new projection operators for the discrete tensor material equations and obtain a compact numerical scheme for the discrete differential operators. This scheme is shown to exhibit significantly reduced numerical dispersion when compared to the standard linear finite element method. We take advantage of the mesh structure on a block-by-block basis to implement these numerical operators efficiently, and achieve computational speed with modest memory requirements when compared to explicit sparse matrix storage. Using the Jacobi–Davidson [G.L.G. Sleijpen, H.A. van der Vorst, A Jacobi–Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 401–425; S.J. Cooke, B. Levush, Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi–Davidson algorithm, J. Comput. Phys. 157 (1) (2000) 350–370] and quasi-minimal residual [R.W. Freund, N.M. Nachtigal, QMR: a quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60 (1991) 315–339] iterative matrix solution algorithms, we solve the resulting discrete matrix eigenvalue equations and demonstrate the convergence characteristics of the algorithm. We validate the model for three-dimensional electromagnetic problems, both cavity eigenvalue solutions and a waveguide scattering matrix calculation.

Cardioprotective Effects of High-Density Lipoproteins

The fact that a low level of high-density lipoprotein (HDL) cholesterol is highly predictive of future cardiovascular events has been established in population studies beyond all reasonable doubt. Furthermore, the evidence is overwhelming that the relationship is one of cause and effect rather than an epiphenomenon, with numerous studies in animals demonstrating that HDL-raising interventions translate into profound reductions in atherosclerosis. Such interventions have included the infusion of both native and reconstituted HDLs into rabbit models of atherosclerosis, the overexpression of apolipoprotein (apo) A-I (the major HDL protein) in transgenic mice and rabbits, and the inhibition of cholesteryl ester transfer protein (CETP) in rabbits. See pages 1325 and 1426 Evidence that raising the level of HDLs is also antiatherogenic in humans is mounting, although there are still relatively few human studies that have directly tested the phenomenon. Fibrates, statins, and niacin all raise the level of HDL cholesterol, and treatment with each of these agents has been shown to be associated with a reduction in future cardiovascular events. Fibrates are especially effective in event reduction in people with insulin resistance or with other features of the metabolic syndrome, although the benefits cannot be explained in terms of the observed HDL raising.1 Statins are effective in reducing events in all subjects, but the benefits can be explained almost completely in terms of the achieved LDL lowering2; the contribution of a statin-induced elevation of HDL is difficult to evaluate. Niacin, the most effective of the currently available HDL-raising agents, has also been shown to reduce cardiovascular events, especially when coadministered with a statin3; but again, other properties of niacin may …

Authors' response

BioelectromagneticsVolume 26, Issue 2 p. 80-80 Authors' Response Authors' response J. Vanderstraeten, Corresponding Author J. Vanderstraeten vdstraeten.j@skynet.be Microwaves UCL, Louvain-la-Neuve, BelgiumAvenue Constant Montold, II B-1200 Bruxelles, Belgium.Search for more papers by this authorA. Vander Vorst, A. Vander Vorst Microwaves UCL, Louvain-la-Neuve, BelgiumSearch for more papers by this author J. Vanderstraeten, Corresponding Author J. Vanderstraeten vdstraeten.j@skynet.be Microwaves UCL, Louvain-la-Neuve, BelgiumAvenue Constant Montold, II B-1200 Bruxelles, Belgium.Search for more papers by this authorA. Vander Vorst, A. Vander Vorst Microwaves UCL, Louvain-la-Neuve, BelgiumSearch for more papers by this author First published: 25 January 2005 https://doi.org/10.1002/bem.20083AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume26, Issue2February 2005Pages 80-80 RelatedInformation

Continuous infusion of factor VIIIc during heart surgery in a patient with haemophilia A

Continuous infusion of factor VIIIc during heart surgery in a patient with haemophilia A

SIMULATIONS OF THE POISSON TYPE PARTIAL DIFFERENTIAL EQUATIONS WHERE THE NODES ARE BOUND BY THE KNIGHT'S MOVES

International Journal of Computational Engineering ScienceVol. 05, No. 01, pp. 25-39 (2004) No AccessSIMULATIONS OF THE POISSON TYPE PARTIAL DIFFERENTIAL EQUATIONS WHERE THE NODES ARE BOUND BY THE KNIGHT'S MOVESRIO HIROWATI SHARIFFUDIN and ITHNIN ABDUL JALILRIO HIROWATI SHARIFFUDINInstitute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia Search for more papers by this author and ITHNIN ABDUL JALILDepartment of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia Search for more papers by this author https://doi.org/10.1142/S1465876304002241Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractIt is very much desired to have subsystems resulting from finite difference modeling of partial differential equations where the matrices are block diagonal as the work required to solve such subsystems is reduced greatly. The simulation nodes in the red/black order and bound by the usual five-point finite difference molecule have their coefficient matrix with such pattern. In this paper, we attempt to have such subsystems for the coefficient matrix for the nodes bound by the nine-point molecule. This can be accomplished by the knight's move. A comparison of the performances between this model and the usual nine-point model is given. We note that the coefficient matrix favors the acceleration of the basic iterative methods.Keywords:Hamiltonian Circuited SimulationsPoisson's EquationsConjugate Gradient SimulationsKnight's Move Model References F. Harary , Graph Theory ( Addison Wesley , New York , 1971 ) . Google ScholarM. R. Hestenes and E. Steifel, Journal of Research of the Nat. Bur. of Stds. 49, 409 (1952). Crossref, Google ScholarD. F. Shanno, Math. of Operations Research 3919780, 244 (1977). Google Scholar E. M. L. Beale , A Derivation of Conjugate Gradients in Numerical Methods for Monlinear Optimization , ed. F. A. Lootsman ( Academic Press , London , 1972 ) . Google ScholarM. J. D. Powell, Math. Prog. 12, 241 (1977). Crossref, Google ScholarE. Polak and G. Riebiere, Revue Francaise Inform. Rech. Operation 16-R1, 35 (1965). Google ScholarA. G. Buckley, Math. Prog. 15, 200 (1978). Crossref, Google ScholarD. Le, Math. Prog. 32, 41 (1985). Crossref, Google Scholar J. W. Daniel , The conjugate Gradient Method for Linear and Nonlinear Operator Equations doctoral thesis: Stanford University . Google ScholarJ. K. Reid, On the method of Conjugate Gradients for The Solution Of Large Sparse Systems of Linear Equations, Proc. Conf. Large Sets of Linear Equations pp. 231–254. Google Scholar R. Bartels and J. W. Daniel , A Conjugate Approach to Nonlinear Elliptic Boundary Value Problem in Irregular Regions , Proc. Conf. Numerical Solution of Differential Equations ( Dundee , 1974 ) . Google Scholar Axelson, O., 1974. On Preconditioning and Convergence Acceleration in Sparse Matrix Problems. CERN 74-10: European Organization for Nuclear research, Data Handling Division . Google Scholar O'Leary D.P.,1975. Hybrid Conjugate Gradient Algorithms, doctoral thesis: Stanford University Pato Alto, California . Google Scholar R. Chandra , Conjugate Gradient Methods for Partial Differential Equations , Research Report 129 ( Connecticut, Department of Comp. Sc., University of New Haven , 1978 ) . Google ScholarP. Concus and G. H. Golub, SIAM J. Num. Anal. 10, 1103 (1973). Crossref, Google Scholar P. Concus and G. H. Golub , A generalized Conjugate Gradient Method For Nonsymmetric Systems of Linear Equations ( Comp. Sc. Dept., Stanford University , 1976 ) . Crossref, Google ScholarD. J. Evans, J.I.M.A. 4, 295 (1968). Google ScholarJ. A. Meijerink and H. A. van der Vorst, Math. Comp. 31, 148 (1977). Google ScholarR. Hirowati Shariffudin and A. R. Abdullah, International Journal of Computer Mathematics 76, (2001). Google ScholarR. Hirowati Shariffudin and A. R. Abdullah, Applied Mathematics Letters 14, 423 (2001). Google Scholar FiguresReferencesRelatedDetails Recommended Vol. 05, No. 01 Metrics History KeywordsHamiltonian Circuited SimulationsPoisson's EquationsConjugate Gradient SimulationsKnight's Move ModelPDF download

Book Review: Iterative Krylow Methods for Large Linear Systems. By H. van der Vorst.

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 84, Issue 3 p. 216-216 Book Review Book Review: Iterative Krylow Methods for Large Linear Systems. By H. van der Vorst. A. Quarteroni, A. Quarteroni Lausanne MilanoSearch for more papers by this author A. Quarteroni, A. Quarteroni Lausanne MilanoSearch for more papers by this author First published: 11 February 2004 https://doi.org/10.1002/zamm.200490001AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume84, Issue3March 2004Pages 216-216 RelatedInformation