Matrix Iterative Method Research Articles

Fast high quality highlight removal using a simplified matrix iteration method

Recently, a global non-smooth optimization method was developed for efficiently eliminating specular highlights from single color image. Although this method was reported to be effective on both natural and medical images, its algorithm’s speed is slow due to the non-smoothness of the objective function. This paper proposes a global smooth optimization method, where two gradient regularization terms are used to describe diffuse and specular component features for texture details. A simplified optimality condition is established and thus a new iteration algorithm for specular highlight removal is proposed. By employing the gradient regularization of diffuse reflection, image texture detail can be preserved during specular highlight removal. Due to the smoothness of the objective function, the proposed smooth optimization algorithm has lower computational complexity and less storage requirement than the global non-smooth optimization algorithm. Furthermore, the proposed iteration algorithm is guaranteed to converge to a global optimal solution under a fixed step length. Experimental results demonstrate that the proposed smooth optimization algorithm is much faster than the non-smooth optimization algorithm. Moreover, the proposed highlight removal algorithm is more effective on benchmark natural images and real laparoscopic images than conventional highlight removal algorithms.

Inverse matrix estimations by iterative methods with weight functions and their stability analysis

In this paper, we construct a parametric family of iterative methods to compute the inverse of a nonsingular matrix. This class is free of inverse operators. We prove the third-order of convergence under some conditions involving the parameter of the family. Moreover, a dynamical analysis is made for the first time to a matrix iterative method, finding intervals of stability, that include but are wider than those found in the convergence analysis. Numerical tests on large random matrices confirm the results found.

A Globally Convergent Iterative Method for Matrix Sign Function and Its Application for Determining the Eigenvalues of a Matrix Pencil

In this research article, we propose a new matrix iterative method with a convergence order of five for computing the sign of a complex matrix by examining the different patterns and symmetry of existing methods. Analysis of the convergence of the method was explored on a global scale, and attraction basins were demonstrated. In addition to this, the asymptotic stability of the scheme was explored.Then, an algorithm for determing thegeneralized eigenvalues for the case of regular matrix pencils was investigated using the matrix sign computation. We performed a series of numerical experiments using numerous matrices to confirm the usefulness and superiority of the proposed method.

Penyusunan Program Komputasi Pengidentifikasi Parameter Dinamik Balok Ditumpu Jepit-Bebas

Operational Modal Analysis (OMA) is a new procedure to identify a structural vibrating system. In this paper, the operational modal analysis based on Ibrahim Time Domain Method. This method requires some displacement data from free vibration response of structure model. Here, a beam with clamped-free condition is used as a test model. Based on Finite Element Method, this beam is divided into 3 elements that consist of 6 degree of freedoms for each element (3 translations and 3 rotations). In this case, a fixed lumped mass is added to each translation node. The beam is excited in its clamped support by sinusoidal displacement during 0.1 s. After 0.1 s, the excitation is stopped and then the displacement data is recorded. Therefore, this condition could be assumed that recorded data represents free vibration response. For this purpose, some computation program was developed to predict the response of free vibration system. First, we make a program SINUS.FOR to produce a sinus displacement function. This function as a support motion is used as an input for program BALKEN.FOR that consist of various program, like Guyan Condensation, Cholesky Decomposition, Jacobi Method, Matrix Iteration Method, Phase Plane Method, Finite Difference Method, Houbolt Method, etc. This entire program is compiled by FORTRAN programming language. Next, the output of BALKEN.FOR that called matrix [A] become an input of program EIGENWERT-ITD.MW which is written in MAPLE programming languages. In this research, it is assumed that only the displacement of x1(t), x2(t) and x3(t) is known. It is known that to identify a system with 6 degrees of freedom, The Ibrahim Time Domain Method requires displacement responses. To fulfill this condition, we need 9 pseudo measurement stations. It means that each station with known displacement response has to be manipulated in such way so that it can produce 3 pseudo displacement response groups. The Result shows that the common error is below 5 %. Except, the damping ratio of mode number 5 is more than 10 %. While the other result can be identified better, especially for the natural frequency is identified very well.

Higher Order Trust Ranking of LinkedIn Accounts with Iterative Matrix Methods

Trust is a fundamental sociotechnological mainstay of the Web today. There is substantial evidence about this since netizens implicitly or explicitly agree to trust virtually every Web service they use ranging from Web-based mail to e-commerce portals. Moreover the methodological framework for trusting individual netizens, primarily their identity and communications, has considerably progressed. Nevertheless, the core of fact checking for human generated content is still far from being substantially automated as most proposed smart algorithms capture inadequately fundamental human traits. One such case is the evaluation of the profile trustworthiness of LinkedIn members based on publicly available attributes available from the platform itself. A trusted profile may indirectly indicate a more suitable candidate since its contents can be easily verified. In this article a first order graph search mechanism for discovering LinkedIn trusted profiles based on a random walker is extended to higher order ranking based on a combination of functional and connectivity patterns. Results are derived for the same benchmark dataset and the first- and higher-order approaches are compared in terms of accuracy.

Coupled physical and magnetodynamic rotational diffusion of a single-domain ferromagnetic nanoparticle suspended in a liquid.

A concise operator form of the Fokker-Planck equation agreeing with that proposed by Weizenecker [Phys. Med. Biol. 63, 035004 (2018)10.1088/1361-6560/aaa186] for the joint orientational distribution of the coupled physical and magnetodynamic rotational diffusion of a single-domain ferromagnetic nanoparticle suspended in a liquid is written from the postulated Langevin equations for the stochastic dynamics. Series expansion of its solution in a complete set yields, using the theory of angular momentum, differential-recurrence equations for statistical moments for coupled motion with uniaxial symmetry of the internal anisotropy-Zeeman energy of a nanoparticle. The numerical results via the matrix iteration method suggest that the susceptibility is adequately approximated by a single Lorentzian with peak frequency given by the inverse integral relaxation time and are discussed in relation to those of the well-known "egg model".

Solving fractional Fredholm integro–differential equations using Legendre wavelets

This paper presents a Legendre wavelet spectral method for solving a type of fractional Fredholm integro–differential equations. The fractional derivative is defined in the Caputo–Prabhakar sense. The derivative of Prabhakar consists of an integro–differential operator that has a Mittag–Leffler function with three parameters in the integration kernel, so it generalizes the Riemann–Liouville and Caputo fractional operators. Moreover, it has many applications in several fields of computational physics. We first derive a matrix method to solve linear problems. In this method, the given linear problem is reduced to a linear system of algebraic equations. The detailed convergence analysis of the proposed matrix method is given. An iterative matrix method is then constructed for nonlinear problems. The nonlinear problem is first replaced with a sequence of linear problems by utilizing the quasilinearization technique. Then, this sequence of problems is successively solved using the matrix method. Numerical examples are included to demonstrate the efficiency and accuracy of the proposed methods.

A new double-step splitting iteration method for certain block two-by-two linear systems

We consider the iterative solution of certain block two-by-two linear systems and introduce a new double-step splitting (NDSS) iteration method. The proposed method is based on the transformed matrix iteration method proposed recently, and obtained by applying two-step and preconditioning techniques for the original linear system. We prove that the NDSS iteration method is convergent under mild conditions. Upper bounds on the spectral radius of the iteration matrix of the NDSS method are presented and the parameters which minimize these bounds are computed. We also consider the inexact NDSS iteration method. The proposed methods are compared theoretically and numerically with some existing ones, which shows the good performance of the NDSS iteration method and its inexact version.

On the parameter selection in the transformed matrix iteration method

Recently, Axelsson and Salkuyeh in (BIT Numerical Mathematics, 59 (2019) 321–342) proposed the transformed matrix iteration (TMIT) method for solving a certain two-by-two block matrices with square blocks. However, they did not present any formula for the optimal parameter of the method which minimizes the spectral radius of the iteration matrix. In this work, we give an upper bound for the spectral radius of the iteration matrix of the method and then compute the parameter which minimizes this upper bound. Numerical results are presented to demonstrate the theoretical results.

Effect of the High-Frequency Laser Radiation on the Nonlinear Optical Properties of n-Type Double δ-Doped GaAs Quantum Wells.

In the present work, the effect of non-resonant intense laser field on the nonlinear optical rectification and second and third harmonic generation of n-type double δ-doped GaAs quantum well is studied in detail. The energy eigenvalues and eigenfunctions of this structure are calculated within the framework of effective mass and envelope function approximations. Analytic formulas for the coefficients of nonlinear optical rectification and second and third harmonic generation are obtained using the compact-density matrix approach (CDMA) and iterative method. Based on this model, our obtained numerical results are reported as a function of incident photon energy for several values of non-resonant intense laser field. The results show that the coefficients of nonlinear optical rectification and second and third harmonic generation are strongly affected by the non-resonant intense laser field.

Conditioning of the matrix-matrix exponentiation

If A has no eigenvalues on the closed negative real axis, and B is arbitrary square complex, the matrix-matrix exponentiation is defined as A B := e log(A)B . It arises, for instance, in Von Newmann’s quantum-mechanical entropy, which in turn finds applications in other areas of science and engineering. In this paper, we revisit this function and derive new related results. Particular emphasis is devoted to its Frechet derivative and conditioning. We propose a new definition of bivariate matrix function and derive some general results on their Frechet derivatives, which hold, not only to the matrix-matrix exponentiation but also to other known functions, such as means of two matrices, second order Frechet derivatives and some iteration functions arising in matrix iterative methods. The numerical computation of the Frechet derivative is discussed and an algorithm for computing the relative condition number of A B is proposed. Some numerical experiments are included.

A matrix CRS iterative method for solving a class of coupled Sylvester-transpose matrix equations

In this paper, we apply Kronecker product and vectorization operator to extend the conjugate residual squared (CRS) method for solving a class of coupled Sylvester-transpose matrix equations. Some numerical examples are given to compare the accuracy and efficiency of the new matrix iterative method with other methods presented in the literature. Numerical results validate that the proposed method can be much more efficient than some existing methods.

Finding solutions for periodic discrete-time generalized coupled Sylvester matrix equations via the generalized BCR method

The periodic discrete-time matrix equations have wide applications in stability theory, control theory and perturbation analysis. In this work, the biconjugate residual algorithm is generalized to construct a matrix iterative method to solve the periodic discrete-time generalized coupled Sylvester matrix equations [Formula: see text] The constructed method is shown to be convergent in a finite number of iterations in the absence of round-off errors. By comparing with other similar methods in practical computation, we give numerical results to demonstrate the accuracy and the numerical superiority of the constructed method.

Self-weight loading of horizontal hydraulic cylinders with axial load

An iterative matrix method is described to determine the deformed shape of a horizontal stepped tube with large axial load, representing a heavy hydraulic cylinder. The method is applicable to both simply supported (pinned-pinned) and clamped-clamped end constraints. The clamped-clamped case is extended to include rotational compliance in the clamps. Using this analysis, radial loads on the piston seals of the cylinder are determined.Comparison is made between the seal loading of a typical large cylinder in pinned-pinned and clamped-clamped configurations, respectively. It is shown that the seal loading can be considerably reduced by the use of the clamped-clamped configuration provided the ends can be well aligned, but that the load is sensitive to angular misalignment.

Matrix iteration method for nonlinear eigenvalue problems with applications

A simple and intuitive matrix iteration method for solving nonlinear eigenvalue problems is described and demonstrated in detail by two problems: (i) the boundary value problem associated with large deflection of a flexible rod, and (ii) the initial value problem associated with normal mode motion of a double pendulum. The two problems are solved by two approaches, the finite difference approach and a continuous realization approach which is similar in spirit to the Rayleigh–Ritz method.

Investigation of an iterative matrix method for the inversion of ARXPS data

Mathematical simulations were used to evaluate an iterative, regularized matrix approach to the recovery of composition depth profiles from ARXPS data containing 1, 3, 5, 7 or 9% noise. The iterative inversion was intended to remove unphysical negative concentration values from the depth profile and to provide some degree of profile sharpening at layer interfaces. It was found that while this procedure worked effectively on data containing just 1% noise, its efficacy diminished as the level of noise increased. Copyright © 2015 John Wiley & Sons, Ltd.

Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations

An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on the possibility to accelerate the iterations in the initial phase of the convergence. Although the effectiveness of our approach is confirmed on the basis of the theoretical point of view, some numerical comparisons in balancing chemical equations, as well as on randomly-generated matrices are furnished.

Relativistic calculation of the electron momentum shift in tunneling ionization

SynopsisWe describe a procedure for the solution of the time-dependent Dirac equation. The procedure is based on the relativistic generalization of the matrix iteration method. We use this procedure to study electron momentum distribution along the laser beam propagation direction for the process of the tunneling ionization of hydrogen atom. We found, in agreement with the experimental observations [1], that relativistic effects lead to appreciable deviation of the distribution from the strict left-right symmetry present in the non-relativistic case. The expectation value of the momentum along the laser beam propagation direction grows linearly with intensity and follows closely the behavior of the expectation value of the kinetic energy divided by the speed of light. These features agree with the experimental results [1].

The matrix iterative methods for solving a class of generalized coupled Sylvester-conjugate linear matrix equations

The conjugate gradients-squared (CGS) method (Sonneveld, 1989) has been considered as an efficient variant of the bi-conjugate gradient (BCG) method. In Vorst (1992), a more smoothly converging variant of the BCG method which keeps the attractive convergence rate of the CGS method was investigated for the solution of certain classes of nonsymmetric linear systems, so-called bi-conjugate gradient stabilized (Bi-CGSTAB) method. In this paper, we will combine these interesting methods for solving the generalized coupled Sylvester-conjugate matrix equations A1XB1+C1Y‾D1=E,A2X‾B2+C2YD2=F after performing suitable transformation by the properties of Kronecker product and vec operator. Some numerical experiments demonstrate that the introduced iterative methods are more efficient than the existing methods.

Relativistic calculation of the electron-momentum shift in tunneling ionization

We describe a procedure for the solution of the time-dependent Dirac equation. The procedure is based on the relativistic generalization of the matrix iteration method. We use this procedure to study electron-momentum distribution along the laser-beam propagation direction for the process of the tunneling ionization of a hydrogen atom. We found, in agreement with the experimental observations [C. T. L. Smeenk, L. Arissian, B. Zhou, A. Mysyrowicz, D. M. Villeneuve, A. Staudte, and P. B. Corkum, Phys. Rev. Lett. 106, 193002 (2011)], that relativistic effects lead to appreciable deviation of the distribution from the strict left-right symmetry present in the nonrelativistic case. The expectation value of the momentum along the laser-beam propagation direction grows linearly with intensity and follows closely the behavior of the expectation value of the kinetic energy divided by the speed of light. These features agree with the experimental results [C. T. L. Smeenk, L. Arissian, B. Zhou, A. Mysyrowicz, D. M. Villeneuve, A. Staudte, and P. B. Corkum, Phys. Rev. Lett. 106, 193002 (2011)].