Faster Convergence for Iterative Solutions to Systems via Three-Part Splittings.

Abstract

For the linear system Ax = y sub o, linear stationery second degree methods, or so-called three-part splittings (which include the first-degree methods of Jacobi, Gauss-Seidel and SOR) are explored for defining the sequence x sub n where x sub n approaches x. By measuring the asymptotic rates of convergence of the sequence, the determination is made when the second-degree method is superior to a corresponding first-degree method. In fact, if B is the iteration matrix of the first degree splitting, then this improvement is analyzed if the spectrum of B is real and when the spectrum of B is pure imaginary.

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1976
Accession Number
ADA027857

Entities

People

  • John De Pillis

Organizations

  • University of California, Riverside

Tags

DTIC Thesaurus Topics

  • Convergence
  • Iterations
  • Linear Systems
  • Mathematics
  • Sequences
  • Spectra
  • Splitting

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Systems Analysis and Design