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RELAXATION METHODS FOR CONVEX PROBLEMS.

Author: Samuel Schechter; STANFORD UNIV CALIF Dept. of COMPUTER SCIENCE.
Publisher: Ft. Belvoir Defense Technical Information Center 16 FEB 1968.
Edition/Format:   Print book : English
Database:WorldCat
Summary:
Extensions and simplifications are made for convergence proofs of relaxation methods for nonlinear systems arising from the minimization of strictly convex functions. This work extends these methods to group relaxation, which includes an extrapolated form of Newton's method, for various orderings. A relatively simple proof is given for cyclic orderings, sometimes referred to as nonlinear overrelaxation, and for  Read more...
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Document Type: Book
All Authors / Contributors: Samuel Schechter; STANFORD UNIV CALIF Dept. of COMPUTER SCIENCE.
OCLC Number: 227480334
Notes: Research supported in part by AEC. Prepared in cooperation with New York Univ., N.Y.
Description: 22 pages

Abstract:

Extensions and simplifications are made for convergence proofs of relaxation methods for nonlinear systems arising from the minimization of strictly convex functions. This work extends these methods to group relaxation, which includes an extrapolated form of Newton's method, for various orderings. A relatively simple proof is given for cyclic orderings, sometimes referred to as nonlinear overrelaxation, and for residual orderings where an error estimate is given. A less restrictive choice of relaxation parameter is obtained than that previously. Applications are indicated primarily to the solution of nonlinear elliptic boundary problems. (Author).

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