Direct and Iterative Linear System Solvers

Gérard Meurant

2026년 4월 · SIAM

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Solving linear systems of equations is ubiquitous in scientific computing; therefore, numerical algorithms for solving them are paramount. This book describes the state of the art in direct and iterative methods for solving nonsingular linear systems of equations. The author considers several variants of elimination methods, classical iterative methods, variants of the conjugate gradient method, and Krylov methods for nonsymmetric systems and describes many preconditioners. Finite precision arithmetic and numerical experiments are emphasized.

Direct and Iterative Linear System Solvers describes and analyzes many numerical experiments with these methods, provides templates of codes for implementing these methods, and introduces more recent techniques like mixed precision and randomization.

This book is intended primarily for applied mathematicians interested in numerical linear algebra, but it will also be of interest to physicists and engineers.

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Gérard Meurant is retired from the French Atomic Energy Commission (CEA), where he worked in applied mathematics from 1970 to 2008. He is the author of more than 60 papers on numerical linear algebra and eight books.