Yan-Fei Jing

University of Electronic Science and Technology of China | UESTC · School of Mathematical Sciences (SMS)

For the simultaneous solution of sequences of linear systems with multiple right-hand sides that result from the discretization of boundary integral equations using the Method of Moments, we show experiments using a robust variant of the block GMRES method. To address memory concerns and improve the convergence of block GMRES, the method combines a...

For the simultaneous solution of sequences of linear systems with multiple right-hand sides that result from the discretization of boundary integral equations using the Method of Moments, we show experiments using a robust variant of the block GMRES method. To address memory concerns and improve the convergence of block GMRES, the method combines a...

The method of moments discretization of boundary integral equations typically leads to dense linear systems. When a single operator is used for multiple excitations, these systems have the same coefficient matrix and multiple right-hand sides (RHSs). Direct solution methods are computationally attractive to use for the solution because they require...

We are concerned with the iterative solution of linear systems with multiple right-hand sides available one group after another with possibly slowly-varying left-hand sides. For such sequences of linear systems, we first develop a new block minimum norm residual approach that combines two main ingredients. The first component exploits ideas from GC...

This paper seeks to position the third-party transaction (TPT) in the macrostructure of Chinese market in terms of Concentration Ratio and Herfindahl-Hirschman Index. By extending both Cournot oligopolistic and Stackelberg oligopolistic competition models, a new oligopolistic competition model is established for China’s TPT market. Based on multidi...

In this paper we propose an acceleration strategy for the Simpler GMRES (SGMRES) method that can considerably improve the convergence of SGMRES method and its variants. The idea is to use the augmentation of approximate errors in SGMRES-E so as to correct the alternative direction behavior of the residual vectors, which hampers the convergence. We...

The deflated block conjugate gradient (D-BCG) method is an attractive approach for the solution of symmetric positive definite linear systems with multiple right-hand sides. However, the orthogonality between the block residual vectors and the deflation subspace is gradually lost along with the process of the underlying algorithm implementation, wh...

We present a performance study of variants of shifted block Krylov subspace methods for the iterative solution of multi-shifted linear systems with multiple right-hand sides given at once. All the methods can solve the whole sequence of systems simultaneously. We analyse the effect of deflated restarting to restore the superlinear convergence rate...

We consider the efficient solution of linear systems with multiple shifts and multiple right-hand sides given simultaneously that arise frequently in large-scale scientific and engineering simulations. We introduce a new shifted block GMRES method that can solve the whole sequence of linear systems simultaneously, it handles effectively the situati...

The original article contained a mistake. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

The solution of large linear systems with multiple right-hand sides given simultaneously is required in many large-scale scientific and engineering applications modelled by either partial differential or boundary integral equations. Block Krylov subspace methods are attractive to use for this problem class as they can overcome the memory bottleneck...

We present new variants of the block GMRES method that combine initial deflation and eigenvalue recycling strategies to remedy some typical convergence problems of block Krylov solvers. The new class of block iterative solvers has the ability to handle the approximate linear dependence of the block of right-hand sides and exploits approximate invar...

The solution of linear systems with multiple shifts and multiple right-hand sides given simultaneously is required in many large-scale scientific and engineering applications. In this paper we introduce new flexible and deflated variants of the shifted block GMRES method for this problem class. The proposed methods solve the whole sequence of linea...

The solution of large linear systems with multiple right-hand sides given simultaneously is required in many large-scale scientific and engineering applications modelled by either partial differential or boundary integral equations. Block Krylov subspace methods are attractive to use for this problem class as they can overcome the memory bottleneck o...

We consider the solution of linear systems with multiple shifts and multiple right-hand sides given simultaneously arising in many large-scale scientific and engineering applications. In this paper we introduce a variant of the shifted block GMRES method that solves the whole sequence of linear systems simultaneously, addresses the situation of ine...

The solution of linear systems with multiple shifts and multiple right-hand sides given simultaneously is required in many large-scale scientific and engineering applications. In this paper we introduce new flexible and deflated variants of the shifted block GMRES method for this problem class. The proposed algorithm solves the whole sequence of li...

Development of flexible variants of the block GMRES method that allow to use variable precondioning for solving sequence of linear systems with multiple shifts and multiple right-hand sides

A variant of the simpler GMRES method is developed for solving shifted linear systems (SGMRES-Sh), exhibiting almost the same advantage of the simpler GMRES method over the regular GMRES method. Because the remedy adapted by GMRES-Sh is no longer feasible for SGMRES-Sh due to the differences between simpler GMRES and GMRES for constructing the resi...

The presentation is about varianta of block Krylov methods for solving linear systems with multiple shifts and multiple right-hand sides.

Block matrix solver for iterative solution of multiple shifts and multiple right-hand sides linear systems.

The restarted block GMRES method with deflated restarting (BGMRES-DR) was proposed by Morgan (2005, Appl: Numer: Math, 54, 222–236) to dump the negative effect of small eigenvalues from the convergence of the block GMRES method. More recently, Wu et al. (2012, SIAM J: Sci: Comput, 34, 2558–2575) introduced the shifted block GMRES method for solving...

In this paper, we study a kind of effective preconditioning technique, which interleaves the incomplete Cholesky (IC) factorization with an approximate minimum degree ordering. An IC factorization algorithm derived from IKJ-version Gaussian elimination is proposed and some details on implementation are presented. Then we discuss the ways to compute...

We consider the solution of large linear systems with multiple right-hand sides using a block GMRES approach. We introduce a new algorithm that effectively handles the situation of almost rank deficient block generated by the block Arnoldi procedure and that enables the recycling of spectral information at restart. The first feature is inherited fr...

The Biconjugate AA-orthogonal residual stabilized method named as BiCORSTAB was proposed by Jing et al. (2009), where the numerical experiments therein demonstrate that the BiCORSTAB method converges more smoothly than the Bi-Conjugate Gradient stabilized (BiCGSTAB) method in some circumstances. In order to further stabilize the convergence behavio...

Linear systems with multiple right-hand sides arise in many applications. To solve such systems efficiently, a new deflated block GCROT($m,k$) method is explored in this paper by exploiting a modified block Arnoldi deflation. This deflation strategy has been shown to have the potential to improve the original deflation which indicates an explicit b...

We consider the solution of large linear systems with multiple right-hand sides using a block GMRES approach. We introduce a new algorithm that effectively handles the situation of almost rank deficient block generated by the block Arnoldi procedure and that enables the recycling of spectral information at restart. The first feature is inherited fr...

We consider the solution of large linear systems with multiple right-hand sides using a block GMRES approach. We introduce a new algorithm that effectively handles the situation of almost rank deficient block generated by the block Arnoldi procedure and that enables the recycling of spectral information at restart. The first feature is inherited fr...

We consider the solution of large linear systems with multiple right-hand sides using a block GMRES approach. We introduce a new algorithm that effectively handles the situation of almost rank deficient block generated by the block Arnoldi procedure and that enables the recycling of spectral information at restart. The first feature is inherited fr...

In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a di...

For solving nonsymmetric linear systems, we attempt to establish symmetric structures in nonsymmetric systems and handle them through the methods devised for symmetric cases. A Biconjugate A-Orthogonal Residual method based on Biconjugate A-Orthonormalization Procedure has been proposed and nominated as BiCOR in [Y.-F. Jing, T.-Z. Huang, Y. Zhang,...

In this paper, two new block ILU preconditioners for block-tridiagonal M-matrices and H-matrices are proposed. Some theoretical properties for the preconditioners are studied and how to construct preconditioners effectively is also discussed. Finally, numerical experiments are also reported for illustrating the efficiency of the presented precondit...

A hybrid finite-element method/method of moments (FEM/MOM) is used to solve 3-D electromagnetic problems. We are focused on the solution to the resulting system of linear equations. Because of the hybrid nature of the FEM/MOM method, the coefficient matrix of the linear system has a very special structure with sparse but indefinite sub-matrices gen...

The Biconjugate 𝐴 -Orthogonal Residual (BiCOR) method carried out in finite precision arithmetic by means of the biconjugate 𝐴 -orthonormalization procedure may possibly tend to suffer from two sources of numerical instability, known as two kinds of breakdowns, similarly to those of the Biconjugate Gradient (BCG) method. This paper naturally...

An incomplete Cholesky (IC) factorization with multi-parameters is presented. The marked virtue of the proposed IC factorization algorithm is to dynamically control the number of nonzero elements in each column of the IC factorization preconditioner L with the help of these involved parameters. Parameter setting strategies are also given. Numerical...

New splitting iterative methods for Toeplitz systems are proposed by means of recently developed matrix splittings based on discrete sine and cosine transforms due to Kailath and Olshevsky [Displacement structure approach to discrete-trigonometric transform-based preconditioners of G. Strang type and of T. Chan type, SIAM J. Matrix Anal. Appl. 26 (...

We report on experiments with a novel family of Krylov subspace methods for solving dense, complex, non-Hermitian systems of linear equations arising from the Galerkin discretization of surface integral equation models in Electromagnetics. By some experiments on realistic radar-cross-section calculation, we illustrate the numerical efficiency of th...

It is very important for generating an orthonormal multiwavelet system to construct a conjugate quadrature filter (CQF). In this paper, a general method of constructing a length- J+1 CQF with multiplicity r and scale a from a length- J CQF is obtained. As a special case, we study generally the construction of a length- J+1 CQF with multiplicity 2 a...

Boundary element discretizations of surface and hybrid surface/volume formulations of electromagnetic scattering problems generate large and dense systems of linear equations that are tough to solve by iterative techniques. The restarted generalized minimal residual (GMRES) method is virtually always used when the systems are non-Hermitian and inde...

An interesting stabilizing variant of the biconjugate A-orthogonal residual (BiCOR) method is investigated for solving non-Hermitian systems of linear equations in electromagnetics. It is naturally based on and inspired by the composite step strategy employed for the composite step biconjugate gradient method. Our motivation is from the point of vi...

We present two iterative algorithms for solving real nonsymmetric and complex non-Hermitian linear systems of equations and that were developed from variants of the nonsymmetric Lanczos method. In this paper, we give the theoretical background of the two iterative methods and discuss their main computational aspects. Using a large number of numeric...

This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods to some extent when applied to the problems and r...

In this paper, we introduce a novel mechanical quadrature method for an efficient solution of weakly singular integral equations arising in two-dimensional electromagnetic scattering problems. This approach is based on and adapted from the recently proposed mechanical quadrature methods in [Extrapolation algorithms for solving mixed boundary integr...

We present economical iterative algorithms built on the Biconjugate $A$-Orthonormalization Procedure for real unsymmetric and complex non-Hermitian systems. The principal characteristics of the developed solvers is that they are fast convergent and cheap in memory. We report on a large combination of numerical experiments to demonstrate that the pr...

The incomplete Cholesky (IC) factorization preconditioning technique is applied to the Krylov subspace methods for solving large systems of linear equations resulted from the use of edge-based finite element method (FEM). The construction of the preconditioner is based on the fact that the coefficient matrix is represented in an upper triangular co...

We present a novel class of Krylov projection methods computed from the Lanczos biconjugate A-Orthonormalization algorithm for the solution of dense complex non-Hermitian linear systems arising from the Method of Moments discretization of electromagnetic scattering problems expressed in an integral formulation. Their competitiveness with other popu...

We introduce a novel variant of the Lanczos method for computing a few eigenvalues of sparse and/or dense non-Hermitian systems arising from the discretization of Maxwell- or Helmholtz-type operators in electromagnetics. We develop a Krylov subspace projection technique built upon short-term vector recurrences that does not require full reorthogona...

Motivated by the celebrated extending applications of the well-established complex Biconjugate Gradient (CBiCG) method to deal with large three-dimensional electromagnetic scattering problems by Pocock and Walker [M.D. Pocock, S.P. Walker, The complex Bi-conjugate Gradient solver applied to large electromagnetic scattering problems, computational c...

In this paper, two multisplitting methods with K+1 relaxed parameters are established for solving a linear system whose coefficient matrix is a large sparse M-matrix or H-matrix and the corresponding convergence behaviors are studied. Then the implementation of these two methods with ILU factorizations as inner splittings is investigated. Finally,...

It is known that the restarted full orthogonalization method (FOM) outperforms the restarted generalized minimum residual method (GMRES) in several circumstances for solving shifted linear systems when the shifts are handled simultaneously. On the basis of the Weighted Arnoldi process, a weighted version of the Restarted Shifted FOM is proposed, wh...

A real square matrix with positive row sums and all its off-diagonal elements bounded below by the corresponding row means is called a $C$-matrix, which is introduced by Peña [Exclusion and inclusion intervals for the real eigenvalues of positive matrices, SIAM J. Matrix Anal. Appl., 26 (2005), pp. 908-917]. In this paper, a new class of nonsingula...

In this paper we consider a novel class of Krylov projection methods computed from the Lanczos biconjugate A- Orthonormalization procedure for the solution of dense complex non-Hermitian linear systems arising from the Method of Moments discretization of Maxwell's equations. We report on experiments on a set of model problems representative of real...

In this paper we consider a novel class of Krylov projection methods computed from the Lanczos biconjugate A- Orthonormalization procedure for the solution of dense complex non-Hermitian linear systems arising from the Method of Moments discretization of Maxwell's equations. We report on experiments on a set of model problems representative of real...

In Ujevi´c [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725–730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss–Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a d...