The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. Computation of estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes.
Gérard Meurant is retired from the French Atomic Energy Commission (CEA), where he worked in applied mathematics from 1970 to 2008. He was research director at the time of his retirement. He is the author of more than 60 papers on numerical linear algebra and six books, including two books co-authored with Gene H. Golub.
Petr Tichż is an associate professor at the Faculty of Mathematics and Physics at Charles University in Prague, Czech Republic. He is the author of more than 27 journal publications and one textbook. His research covers a variety of topics in numerical linear algebra, optimization, approximation of functions, and round-off error analysis of algorithms.
