zbMATH — the first resource for mathematics

A family of quasi-Newton methods with direct factorization of secant updated matrices and preservation of sparsity and their convergence. (Chinese. English summary) Zbl 0918.65036
Summary: I. D. L. Bogle and J. D. Perkins [SIAM J. Sci. Stat. Comput. 11, No. 4, 621-630 (1990; Zbl 0749.65033)] have proposed a quasi-Newton method based on a minimal relative change which retains the sparsity of secant updated matrices. A family of new methods with direct factorization of secant updated matrices and the preservation of sparsity are presented. A set of numerical examples show their advantages. Under proper conditions, the method can be proved to be $$Q$$-superlinear convergent.
MSC:
 65H10 Numerical computation of solutions to systems of equations