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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Krylov subspace methods for solving large unsymmetric linear systems
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by Y. Saad PDF
Math. Comp. 37 (1981), 105-126 Request permission


Some algorithms based upon a projection process onto the Krylov subspace ${K_m} = \operatorname {Span}({r_0},A{r_0}, \ldots ,{A^{m - 1}}{r_0})$ are developed, generalizing the method of Conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldi’s algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace ${K_m}$ and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 105-126
  • MSC: Primary 65F10
  • DOI:
  • MathSciNet review: 616364