×

zbMATH — the first resource for mathematics

Convergence of the conjugate gradient method with computationally convenient modifications. (English) Zbl 0178.18302

PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Daniel, J. W.: (a) The conjugate gradient method for linear and nonlinear operator equations. Stanford University Ph. D. thesis, August 1965; (b) The conjugate gradient method for linear and nonlinear operator equations. J. Soc. Indust. Appl. Math., Ser. B, Numer. Anal.4, 10–26 (1967). · Zbl 0154.40302
[2] Engeli, M., Th. Ginsburg, H. Rutishauser, andE. Stiefel: Refined iterative methods for the computation of the solution and eigenvalues of self-adjoint boundary value problems. Mitteilungen aus dem Institut für angewandte Mathematik, Nr. 8, 1959 · Zbl 0089.12103
[3] Fletcher, R., andM. J. D. Powell: A rapidly convergent descent method for minimization. Comput. J.6, 163–169 (1963). · Zbl 0132.11603
[4] —-, andC. M. Reeves: Function minimization by conjugate gradients. Comput. J.7, 149–154 (1964). · Zbl 0132.11701 · doi:10.1093/comjnl/7.2.149
[5] Greenspan, D., andS. V. Farter: Mildly nonlinear elliptic partial differential equations and their numerical solution, II. Numer. Math.7, 129–147 (1965). · Zbl 0135.38302 · doi:10.1007/BF01397686
[6] Hestenes, M. R., andE. Stiefel: Method of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards49, 409–436 (1952). · Zbl 0048.09901
[7] Powell, M. J. D.: (a) An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J.7, 155–162 (1964); (b) A method for minimizing a sum of squares of nonlinear functions without calculating derivatives. Comput. J.7, 303–307 (1964). · Zbl 0132.11702 · doi:10.1093/comjnl/7.2.155
[8] Rosenbrock, H. H.: An automatic method for finding the greatest or the least value of a function. Comput. J.3, 175–184 (1960). · doi:10.1093/comjnl/3.3.175
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.