GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Applied numerical linear algebra
Applied numerical linear algebra
Guest Editors' Introduction: The Top 10 Algorithms
Computing in Science and Engineering
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Inexact Krylov Subspace Methods for Linear Systems
SIAM Journal on Matrix Analysis and Applications
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
A Dynamical Tikhonov Regularization for Solving Ill-posed Linear Algebraic Systems
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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A mathematical procedure for finding a closed-form double optimal solution (DOS) of an n-dimensional linear equations system Bx=b is developed, which expresses the solution in an m-dimensional affine Krylov subspace with undetermined coefficients, and two optimization techniques are used to determine these coefficients in closed-form. To find the DOS, it is very time saving without the need of any iteration; in practice, we only need to invert an mxm matrix one time, where m@?n. The DOS is not exactly equal to the exact solution, but it can provide an acceptable approximate solution of linear equations system, whose applicable range is identified. Some properties are analyzed that the DOS is an exact solution of a projected linear system of Bx=b onto the affine Krylov subspace. The tests for large scale problems demonstrate the efficiency of DOS on non-sparse linear systems.