Block Row Research Articles

A direct method to solve block banded block Toeplitz systems with non-banded Toeplitz blocks

A fast solution algorithm is proposed for solving block banded block Toeplitz systems with non-banded Toeplitz blocks. The algorithm constructs the circulant transformation of a given Toeplitz system and then by means of the Sherman–Morrison–Woodbury formula transforms its inverse to an inverse of the original matrix. The block circulant matrix with Toeplitz blocks is converted to a block diagonal matrix with Toeplitz blocks, and the resulting Toeplitz systems are solved by means of a fast Toeplitz solver. The computational complexity in the case one uses fast Toeplitz solvers is equal to ξ ( m , n , k ) = O ( m n 3 ) + O ( k 3 n 3 ) flops, there are m block rows and m block columns in the matrix, n is the order of blocks, 2 k + 1 is the bandwidth. The validity of the approach is illustrated by numerical experiments.

A Krylov Method for the Delay Eigenvalue Problem

The Arnoldi method is currently a very popular algorithm to solve large-scale eigenvalue problems. The main goal of this paper is to generalize the Arnoldi method to the characteristic equation of a delay-differential equation (DDE), here called a delay eigenvalue problem (DEP). The DDE can equivalently be expressed with a linear infinite-dimensional operator whose eigenvalues are the solutions to the DEP. We derive a new method by applying the Arnoldi method to the generalized eigenvalue problem associated with a spectral discretization of the operator and by exploiting the structure. The result is a scheme where we expand a subspace not only in the traditional way done in the Arnoldi method. The subspace vectors are also expanded with one block of rows in each iteration. More important, the structure is such that if the Arnoldi method is started in an appropriate way, it has the (somewhat remarkable) property that it is in a sense independent of the number of discretization points. It is mathematically equivalent to an Arnoldi method with an infinite matrix, corresponding to the limit where we have an infinite number of discretization points. We also show an equivalence with the Arnoldi method in an operator setting. It turns out that with an appropriately defined operator over a space equipped with scalar product with respect to which Chebyshev polynomials are orthonormal, the vectors in the Arnoldi iteration can be interpreted as the coefficients in a Chebyshev expansion of a function. The presented method yields the same Hessenberg matrix as the Arnoldi method applied to the operator.

Stochastic iterative projection methods for large linear systems

We suggest a randomized version of the projection methods belonging to the class of a “row-action” methods which work well both for systems with quadratic nonsingular matrices and for overdetermined systems. These methods belong to a type known as Projection on Convex Sets methods. Here we present a method beyond the conventional Markov chain based Neumann–Ulam scheme. The main idea is in a random choice of blocks of rows in the projection method so that in average, the convergence is improved compared to the conventional periodic choice of the rows. We suggest an acceleration of the row projection method by using the Johnson–Lindenstrauss (J–L) theorem to find, among the randomly chosen rows, in a sense an optimal row. We extend this randomized method for solving linear systems coupled with systems of linear inequalities. Applied to finite-difference approximations of boundary value problems, the method appears to be an extremely efficient Random Walk algorithm whose convergence is exponential, and the cost does not depend on the dimension of the matrix. In addition, the algorithm calculates the solution in all grid points, and is easily parallelizable.

Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix

Closed-form formulas are derived for the rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix. A variety of consequences on the nonsingularity, nullity and definiteness of the submatrices are also presented. h stand for the sets of all m×n complex matrices and all m×m Hermitian complex matrices, respectively. The symbols A ∗ , r(A) and R(A) stand for the conjugate transpose, rank and range (column space) of a matrix A 2 C m×n , respectively. (A, B ) denotes a row block matrix consisting of A and B. The inertia of a Hermitian matrix A is defined to be the triplet In(A) = {i+(A), i−(A), i0(A)}, where i+(A), i−(A) and i0(A) are the numbers of the positive, negative and zero eigenvalues of A counted with multiplicities, respectively. It is obvious that r(A) = i+(A) + i−(A). We write A > 0 (A > 0) if A is Hermitian positive (nonnegative) definite. Two Hermitian matrices A and B of the same size are said to satisfy the inequality A > B (A > B) in the Lowner partial ordering if A B is positive (nonnegative) definite. The Moore-Penrose inverse of A 2 C m×n , denoted by A † , is defined to be the unique solution X of the four matrix equations

EXPERIMENTAL INVESTIGATION ON MAKHOOL DAM STILLING BASIN

This research is an experimental investigation on the hydraulic performance of the combined hydraulic jump and plunge pool stilling basin operating under high head for Makhool Dam. Two series of tests are carried out; the first series are on the model as it is designed, while the second series are on a modified model by adding two rows of chute blocks.
 (81) Experiments are performed on both models. The results indicated that for the first model the stilling basin length can be reduced and there is negative pressure at the beginning of the jump on the sloping apron with high turbulence and unstable water surface. After adding the chute blocks, the tests of the second model indicated that the stilling basin length can be reduced and all pressures are positive with reasonably stable water surface as well as lower turbulence. Therefore, chute blocks are recommended to be added

CsegGraph: a graph colouring instance generator

The implementation of a graph generator associated with the estimation of mathematical derivatives is described. The graph colouring instances are obtained as intersection graphs G Π(A) of the sparsity pattern of A∈ℜ m×n with row partition Π. The size of the graph is dependent on the row partition; the number of vertices can be varied between the number of columns (using single block row partition Π=Π1) and the number of nonzero entries of A (using m-block row partition Π=Π m ). The chromatic number of the generated graph instances satisfy . A summary of colouring results on the ColSegSet problems is presented. We also show that the main idea of the graph instance generator can be extended to general undirected graphs.

Heat transfer and flow temperature measurements in a rotating triangular channel with various rib arrangements

In the present study, the regionally-averaged heat transfer coefficients and flow temperature distributions were measured in an equilateral triangular channel with three different rib arrangements (α = 45, 90 and 135°). To measure regionally-averaged heat transfer coefficients in the channel, two rows of copper blocks and a single heater were installed on two ribbed walls. The fluid temperature distributions were obtained using a thermocouple-array. The rotation number ranged from 0.0 to 0.1 with a fixed Reynolds number of 10,000. For the 90° ribs, the heat transfer coefficients on the pressure side surface were increased significantly with rotation, while the suction side surface had lower heat transfer coefficients than the stationary channel. For the angled ribs, rib-induced secondary flow dominated the heat transfer characteristics and high heat transfer rates were observed on the regions near the inner wall for the 45° angled ribs and near the leading edge for the 135° angled ribs.

Identification of Bilinear Systems With White Noise Inputs: An Iterative Deterministic-Stochastic Subspace Approach

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this technical brief, a new subspace state space system identification algorithm for multi-input multi-output bilinear systems driven by white noise inputs is introduced. The new algorithm is based on a uniformly convergent Picard sequence of linear deterministic-stochastic state space subsystems which are easily identifiable by any linear deterministic-stochastic subspace algorithm such as MOESP, N4SID, CVA, or CCA. The key to the proposed algorithm is the fact that the bilinear term is a second-order white noise process. Using a standard linear Kalman filter model, the bilinear term can be estimated and combined with the system inputs at each iteration, thus leading to a linear system with extended inputs of dimension <formula formulatype="inline"><tex Notation="TeX">$m(n+1)$</tex></formula>, where <formula formulatype="inline"> <tex Notation="TeX">$n$</tex></formula> is the system order and <formula formulatype="inline"> <tex Notation="TeX">$m$</tex></formula> is the dimension of the inputs. It is also shown that the model parameters obtained with the new algorithm converge to those of the true bilinear model. Moreover, the proposed algorithm has the same consistency conditions as the linear subspace identification algorithms when <formula formulatype="inline"><tex Notation="TeX">$i\rightarrow\infty$</tex> </formula>, where <formula formulatype="inline"><tex Notation="TeX">$i$</tex> </formula> is the number of block rows in the past/future block Hankel data matrices. Typical bilinear subspace identification algorithms available in the literature cannot handle large values of <formula formulatype="inline"> <tex Notation="TeX">$i$</tex></formula>, thus leading to biased parameter estimates. Unlike existing bilinear subspace identification algorithms whose row dimensions in the data matrices grow exponentially, and hence suffer from the “curse of dimensionality,” in the proposed algorithm the dimensions of the data matrices are comparable to those of a linear subspace identification algorithm. A case study is presented with data from a heat exchanger experiment. </para>

Development an Analytical Performance Models for Matrix Multiplication on Distributing Systems

In this paper, we suggest a mechanism for implementing a distributed application using RMI based on JAVA threads. The application is parallel matrices multiplication depending on distributed the products block of rows and columns on different machines. One server and seven clients are run to find the product of matrix multiplication. The server distributes the determine blocks of rows and columns on the registered clients. The clients return their product blocks to a server, whichcalculate the final product of matrix multiplication. Applications of this type will allow loaded servers to transfer part of the load to clients to exploit the computing power available at client side. Experimental result shows that the speed up ratio is equals 9 or the computation time of matrix multiplication with size of 2048 X 2048 is reduced by 89 % by using 7-client.

How In-Situ Combustion Works in a Fractured System

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 117645, "How In-Situ Combustion Process Works in a Fractured System: Two-Dimensional, Core- and Block-Scale Simulation," by H. Fadaei, Institut Francais du Petrole; M. Quintard and G. Debenest, l'Institut de Mecanique des Fluides de Toulouse; G. Renard, SPE, Institut Francais du Petrole; and A.M. Kamp, SPE, Open and Experimental Center for Heavy Oil, prepared for the 2008 SPE International Thermal Operations and Heavy Oil Symposium, Calgary, 20-23 October. The paper has not been peer reviewed. Simulation of an in-situ-combustion (ISC) process was performed for a fractured system at core and matrix-block scales. The aim of this work was to predict the ISC ignition/propagation conditions, understand the mechanism of oil recovery, and provide guidelines for ISC scaleup for a fractured system. The study was of a fine-grid single-porosity multiphase multicomponent system and used a thermal-reservoir simulator. Introduction Heavy-oil recovery from fractured carbonate reservoirs (one-third of global heavy-oil resources) has been low because of the complexity of such reservoirs. The recovery mechanism and the reservoir and operational conditions at which combustion can propagate in fractured systems are not understood clearly. This study investigated ISC-propagation conditions and oil-recovery mechanisms at the fractured-core scale, and investigated the process at the block scale to address the 2D behavior of ISC at large scale. The objective was to determine the dominant processes in combustion propagation at the block scale and the characteristics of different fronts that exist. Model Four phases exist in crude-oil combustion in porous media: oil, gas, water, and solid. The oil and gas phases are multicomponent (i.e., hydrocarbon components), the water is a vapor, and the solid phase contains inert solid and coke. Reactions take place in the oil, in the gas, and on the surface of the solid phase (when coke is present). Coke is formed by pyrolysis and deposited on the solid surface. Reactions in oil and gas phases are homogeneous, but the coke reaction is heterogeneous. Simulation Oil Combustion in a Fractured System. Ignition/propagation conditions of the combustion front in a fractured system and the governing production mechanisms were studied. The simulation model is presented in Fig. 1, and the input data for the model are detailed in Table 1 of the full-length paper. A vertical core was used to mimic a top-down process. The core had no temperature losses at its boundaries, and the top row of blocks was heated with a constant heating rate. Heat injection was maintained for 24 minutes, until ignition occurred. This time was considered to be approximately that used in a nonfractured core.

Design of stilling basin for circular pipe outlets

Experimental work leading to the design of a stilling basin for pipe outlets is reported in this paper. The stilling basin designed on the basis of present study has been compared with the stilling basin design proposed by Garde et al. in 1986. The experiments were performed by taking two pipe outlets of 10 and 7.5 cm diameter and varying inflow Froude numbers. In the present study, the new design is arrived at by conducting a systematic experimentation on the various stilling basin models and keeping the basin floor at the invert level of the pipe outlet. The location as well as the arrangements of appurtenances, such as a wedge-shaped splitter block, modified grid, row of wedge-shaped baffle blocks, and end sill, were also varied in the experiments. A nondimensional number has been defined to compare the performance of the stilling basin models on the basis of developed scour downstream of the basin. The performance of the proposed stilling basin (model M-71) is much better as compared with that of the stilling basin G-D* proposed by Garde et al. in 1986.

Approximation and continuity of Moore–Penrose inverses of orthogonal row block matrices

A well-known result on the Moore–Penrose inverse of row block matrix asserts that [ A , B ] † = A † B † if and only if A ∗ B = 0 , where ( · ) † and ( · ) ∗ denote the Moore–Penrose inverse and the conjugate transpose of a matrix, respectively. In this paper, we show some norm inequalities for the difference [ A , B ] † - A † B † , and then use the norm inequalities to investigate approximation and continuity of [ A , B ] † as A ∗ B → 0 .

Odor-Baited Trap Trees: A Novel Management Tool for Plum Curculio (Coleoptera: Curculionidae)

The plum curculio, Conotrachelus nenuphar (Herbst) (Coleoptera: Curculionidae), one of the most important pests of apple (Malus spp.) in eastern and central North America, historically has been managed in New England apple orchards by three full block insecticide applications. Efforts to reduce insecticide inputs against plum curculio include perimeter row sprays, particularly after petal fall, to control immigrating adults. The odor-baited trap tree approach represents a new reduced input strategy for managing plum curculio based on the application of insecticides to a few perimeter-row trap trees rather than the entire perimeter row or full orchard block. Here, we compared the efficacy of a trap tree approach with perimeter row treatments to manage populations after petal fall in commercial apple orchards in 2005 and 2006. Injury was significantly greater in trap trees compared with unbaited perimeter row treated trees in both years of the study. In 2005, heavy rains prevented growers from applying insecticide applications at regular intervals resulting in high injury in nearly all blocks regardless of type of management strategy. In 2006, both the trap-tree and perimeter-row treatments prevented penetration by immigrating populations and resulted in economically acceptable levels of injury. The trap tree management strategy resulted in a reduction of approximately 70% total trees being treated with insecticide compared with perimeter row sprays and 93% compared with standard full block sprays.

Generalized Combining Method for Design of Quasi-Cyclic LDPC Codes

A generalization of the Chinese Remainder Theorem (CRT) combining method is proposed to design much more and better quasi-cyclic (QC) LDPC codes when the parity check matrices of the component codes are given. It can design a much larger class of QC-LDPC codes with similar performance by loosening the condition for determining the intermediate parameters. By permuting the block rows of the parity check matrices of the component codes, a lot of QC-LDPC codes with much less 6-cycles and better performance can be designed. At a BER of 10-6 some QC-LDPC codes designed by the generalized combining method outperform those designed by the CRT combining method by 0.5 dB.

Markov Chains with Hybrid Repeating Rows - Upper-Hessenberg, Quasi-Toeplitz Structure of the Block Transition Probability Matrix

In this paper we consider discrete-time multidimensional Markov chains having a block transition probability matrix which is the sum of a matrix with repeating block rows and a matrix of upper-Hessenberg, quasi-Toeplitz structure. We derive sufficient conditions for the existence of the stationary distribution, and outline two algorithms for calculating the stationary distribution.

Markov Chains with Hybrid Repeating Rows - Upper-Hessenberg, Quasi-Toeplitz Structure of the Block Transition Probability Matrix

In this paper we consider discrete-time multidimensional Markov chains having a block transition probability matrix which is the sum of a matrix with repeating block rows and a matrix of upper-Hessenberg, quasi-Toeplitz structure. We derive sufficient conditions for the existence of the stationary distribution, and outline two algorithms for calculating the stationary distribution.

On nonsymmetric saddle point matrices that allow conjugate gradient iterations

Linear systems in saddle point form are usually highly indefinite,which often slows down iterative solvers such as Krylov subspace methods. It has been noted by several authors that negating the second block row of a symmetric indefinite saddle point matrix leads to a nonsymmetric matrix \({{\mathcal A}}\) whose spectrum is entirely contained in the right half plane. In this paper we study conditions so that \({{\mathcal A}}\) is diagonalizable with a real and positive spectrum. These conditions are based on necessary and sufficient conditions for positive definiteness of a certain bilinear form,with respect to which \({{\mathcal A}}\) is symmetric. In case the latter conditions are satisfied, there exists a well defined conjugate gradient (CG) method for solving linear systems with \({{\mathcal A}}\). We give an efficient implementation of this method, discuss practical issues such as error bounds, and present numerical experiments.

T-shape homogenous block patterns for the two-dimensional cutting problem

This paper presents an algorithm for unconstrained T-shape homogenous block cutting patterns of rectangular pieces. A vertical cut divides the stock sheet into two segments. Each segment consists of sections that have the same length and direction. A section contains a row of homogenous blocks. A homogenous block consists of homogenous strips of the same piece type. Each cut on the block produces just one strip. The directions of two strips cut successively from a block are either parallel or orthogonal. The algorithm uses a dynamic programming recursion to generate optimal blocks, solves knapsack problems to obtain the block layouts on the sections and the section layout on segments of various lengths, and optimally selects two segments to compose the cutting pattern. The computational results indicate that the algorithm is efficient in improving material usage, and the computation time is reasonable.

A new solution expressed in terms of UTD coefficients for the multiple diffraction of spherical waves by a series of buildings

A new formulation expressed in terms of Uniform Theory of Diffraction (UTD) coefficients for the prediction of the multiple diffraction caused by a series of buildings modeled as wedges, considering spherical‐wave incidence, is presented. The solution, which has a certain heuristic nature, is validated with numerical results from technical literature and the particular cases of diffraction by buildings modeled as absorbing knife edges, as well as the one in which the mentioned buildings are replaced by flat‐roofed parallel rows of blocks (building rows in cross sections considered to be rectangular in shape) are also analyzed. The computing time is reduced over existing formulations, especially when the number of buildings is large, and the results can be applied in the development of theoretical models, in order to predict a more realistic path loss in urban environments when multiple‐building diffraction has to be considered.

Bone breccias, bone dumps, and sedimentary sequences of the western Limeworks, Makapansgat, South Africa

The sediments in the western side of the Makapansgat Limeworks were either precipitated as speleothems, represented in the earlier massive deposits, or were deposited as coarsening clastic sediments, mainly representing later deposits. Between the earlier deposits and the main sedimentary phase, the stratigraphic sequence was inverted twice to a considerable height by the unusual deposition of subaqueous speleothem. Bone-bearing deposits, including the Main Quarry Bone Breccia and the well-known Grey Breccia belong, in time, to the lower part of the clastic deposits called the Red Silts. Australopith fossils have been found in the Grey Breccia dumped material and, in situ, from the dolomite clast breccia on the Main Quarry entrance buttress. Whatever the problems may be in provenancing some of the material from the Limeworks dumps, there is no doubt that the three rows of blocks on the southern side of the dumps belong to the Grey Breccia, and other rows contain red sediment sufficient for them to be safely associated with the Red Silts. There is no reason why this material should not be prepared with confidence as to its stratigraphic provenance. In any case, stratigraphic evidence, presented here, shows that there is little difference in time between the deposition of the bone-bearing breccias.