Journal ArticleDOI
The Tchebychev iteration for nonsymmetric linear systems
TLDR
In this paper, an iterative method for solving nonsymmetric linear systems based on the Tchebychev polynomials in the complex plane is discussed, and the iteration is shown to converge whenever the eigenvalues of the linear system lie in the open right half complex plane.Abstract:
In this paper an iterative method for solving nonsymmetric linear systems based on the Tchebychev polynomials in the complex plane is discussed. The iteration is shown to converge whenever the eigenvalues of the linear system lie in the open right half complex plane. An algorithm is developed for finding optimal iteration parameters as a function of the convex hull of the spectrum.read more
Citations
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Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
TL;DR: In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist.
Journal ArticleDOI
QMR: a quasi-minimal residual method for non-Hermitian linear systems
TL;DR: A novel BCG-like approach, the quasi-minimal residual (QMR) method, which overcomes the problems of BCG is presented and how BCG iterates can be recovered stably from the QMR process is shown.
Journal ArticleDOI
Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
TL;DR: A class of iterative algorithms for solving systems of linear equations where the coefficient matrix is nonsymmetric with positive-definite symmetric part, modelled after the conjugate gradient method, are considered.
Journal ArticleDOI
Fast iterative methods for discrete-ordinates particle transport calculations
Marvin L. Adams,Edward W. Larsen +1 more
TL;DR: This Review discusses the theoretical foundations of the development of acceleration methods for iterative convergence of discrete-ordinates simulations, the important results that have been accomplished, and remaining open questions.
Journal ArticleDOI
Iterative solution of linear systems in the 20th century
TL;DR: In this article, the main research developments in the area of iterative methods for solving linear systems during the 20th century are described and compared, and the most signicant contributions during the past century are compared to one another.
References
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Journal ArticleDOI
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.
Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Book
Matrix iterative analysis
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
Book
Iterative Solution of Large Linear Systems
TL;DR: The ASM preconditioner B is characterized by three parameters: C0, ρ(E) , and ω , which enter via assumptions on the subspaces Vi and the bilinear forms ai(·, ·) (the approximate local problems).