Some history of the conjugate gradient and Lanczos algorithms: 1948-1976. (English) Zbl 0673.65017

There are reviewed 291 papers of 275 authors considering conjugate gradient algorithms for linear and nonlinear systems using different choices of the inner product as well as the Lanczos algorithm for eigenvalue problems during the period from the original development to the widespread application in the mid-1970s. “Since that time, the algorithms have been further refined and have become a basic tool for solving a wide variety of problems on a wide variety of computer architectures.” In particular, the reviews concern preconditioning, matrix splittings and applications to optimization problems and partial differential equations. A special survey is given to the early quarterly reports of the National Applied Mathematics Laboratories from 1949 to 1952.
Reviewer: L.Berg


65F10 Iterative numerical methods for linear systems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65-03 History of numerical analysis
65H10 Numerical computation of solutions to systems of equations
01A65 Development of contemporary mathematics
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