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