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A new block triangular preconditioner for three-by-three block saddle-point problem

Jun Li, Xiangtuan Xiong (2024)

Applications of Mathematics

In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties are also discussed....

A new optimized iterative method for solving M -matrix linear systems

Alireza Fakharzadeh Jahromi, Nafiseh Nasseri Shams (2022)

Applications of Mathematics

In this paper, we present a new iterative method for solving a linear system, whose coefficient matrix is an M -matrix. This method includes four parameters that are obtained by the accelerated overrelaxation (AOR) splitting and using the Taylor approximation. First, under some standard assumptions, we establish the convergence properties of the new method. Then, by minimizing the Frobenius norm of the iteration matrix, we find the optimal parameters. Meanwhile, numerical results on test examples...

A numerical study on Neumann-Neumann methods for hp approximations on geometrically refined boundary layer meshes II. Three-dimensional problems

Andrea Toselli, Xavier Vasseur (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we present extensive numerical tests showing the performance and robustness of a Balancing Neumann-Neumann method for the solution of algebraic linear systems arising from hp finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in three dimensions. The numerical results are in good agreement with the theoretical bound for the condition number of the preconditioned operator derived in [Toselli and Vasseur, IMA J. Numer. Anal.24 (2004)...

A one parameter method for the matrix inverse square root

Slobodan Lakić (1997)

Applications of Mathematics

This paper is motivated by the paper [3], where an iterative method for the computation of a matrix inverse square root was considered. We suggest a generalization of the method in [3]. We give some sufficient conditions for the convergence of this method, and its numerical stabillity property is investigated. Numerical examples showing that sometimes our generalization converges faster than the methods in [3] are presented.

A parallel projection method for linear algebraic systems

Fridrich Sloboda (1978)

Aplikace matematiky

A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.

A real-valued block conjugate gradient type method for solving complex symmetric linear systems with multiple right-hand sides

Yasunori Futamura, Takahiro Yano, Akira Imakura, Tetsuya Sakurai (2017)

Applications of Mathematics

We consider solving complex symmetric linear systems with multiple right-hand sides. We assume that the coefficient matrix has indefinite real part and positive definite imaginary part. We propose a new block conjugate gradient type method based on the Schur complement of a certain 2-by-2 real block form. The algorithm of the proposed method consists of building blocks that involve only real arithmetic with real symmetric matrices of the original size. We also present the convergence property of...

Currently displaying 41 – 60 of 124