EFFICIENT IMPLEMENTATION OF MINIMAL POLYNOMIAL AND REDUCED RANK EXTRAPOLATION METHODS

[摘要] The minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two very effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equations. Their definitions involve some linear least-squares problems, and this causes difficulties in their numerical implementation. In this work timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems, among them a hypersonic flow problem involving chemical reactions.

[发布日期] 1991-09-24

[关键词] EXTRAPOLATION;CONVERGENCE ACCELERATION;MINIMAL POLYNOMIAL EXTRAPOLATION;REDUCED RANK EXTRAPOLATION;VECTOR SEQUENCES;LINEAR AND NONLINEAR SYSTEMS;FIXED-POINT ITERATIVE TECHNIQUES;LEAST SQUARES;QR FACTORIZATION