Abstract. We present a detailed convergence analysis of preconditioned MINRES for approximately solving the linear systems that arise when Rayleigh Quotient Iteration is used to compute the lowest eigenpair of a symmetric positive definite matrix. We provide insight into the “slow start” of MINRES iteration in both a qualitative and quantitative way, and show that the convergence of MINRES main...

The laminin 5 (Ln-5) gamma2 chain and matrix metalloproteinases (MMPs) MMP-2 and membrane type 1 (MT1)-MMP act cooperatively and are required for highly aggressive melanoma cells to engage in vasculogenic mimicry when cultured on a three-dimensional matrix. Furthermore, generation of Ln-5 gamma2 chain promigratory fragments by MMP-2 and MT1-MMP proteolysis is necessary for an aggressive tumor c...

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references. Keywords—Backward MPSD iterative matrix, Jacobi itera...

We present a parallel Preconditioned BiConjugate Gradient Stabilized(BICGstab) solver for the Poisson problem. Given a real, nosymmetric and positive definite coefficient matrix , the parallized Preconditioned BICGstab -solver is able to find a solution for that system by exploiting the massive compute power of todays GPUs.Comparing sequential CPU implementations and that algorithm.we achieve a...

We present a parallel Preconditioned BiConjugate Gradient Stabilized(BICGstab) solver for the Poisson problem. Given a real, nosymmetric and positive definite coefficient matrix , the parallized Preconditioned BICGstab -solver is able to find a solution for that system by exploiting the massive compute power of todays GPUs.Comparing sequential CPU implementations and that algorithm.we achieve a...

Abstract In this paper, an augmentation preconditioner for asymmetric saddle point problems with singular (1,1) blocks is introduced on the base of the recent article by He and Huang [Two augmentation preconditioners for nonsymmetric and indefinite saddle point linear systems with singular (1, 1) blocks, Comput. Math. Appl., 62 (2011) 87-92]. We study the spectral characteristics of the precond...

The convergence features of a preconditioned algorithm for the convection-diffusion equation based on its diffusion part are considered. An analysis of the distribution of the eigenvalues of the preconditioned matrix and of the fundamental parameters of convergence are provided, showing the existence of a proper cluster of eigenvalues and the superlinear behavior of preconditioned iterations. T...

In this paper, we consider solving the robust linear regression problem. We show that IRLS and Newton method can each be combined with preconditioned conjugate gradient least squares method to solve large, sparse, rectangular systems of linear, algebraic equations eeciently. We deene a new function that leads to a cheap preconditioner. Further, for this function, we show that the upper bound on...

We develop a general convergence theory for the generalized minimal residual method for least squares problems preconditioned with inner iterations. The inner iterations are performed by stationary iterative methods. We also present theoretical justifications for using specific inner iterations such as the Jacobi and SOR-type methods. The theory is improved particularly in the rankdeficient cas...

The convergence features of a preconditioned algorithm for the convection-diffusion equation based on its diffusion part are considered. Analyses of the distribution of the eigenvalues of the preconditioned matrix in arbitrary dimensions and of the fundamental parameters of convergence are provided, showing the existence of a proper cluster of eigenvalues. The structure of the cluster is not in...