BLOCK ITERATIVE METHODS FOR TWO-CYCLIC MATRIX EQUATIONS WITH SPECIAL APPLICATION TO THE NUMERICAL SOLUTION OF THE SECOND-ORDER SELF-ADJOINT ELLIPTIC PARTIAL DIFFERENTIAL EQUATION IN TWO DIMENSIIONS

Technical Report · Sun Apr 01 04:00:00 EST 1962

OSTI ID:4812735

Hageman, L A

An investigation was made to determine whether a cyclically reduced system of equations or the original system may be solved by an iterative method in the most efficient manner. Sohroder and Varga used the special form of a 2- cyclic matrix to obtain improvements in the convergence rate for certain point iteration techniques. It is shown that improvements in the rate of convergence may also be obtained for various block iteration techniques and that the cyclic reduction process leads to an efficient method of solution for the two- dimensional self-adjoint second-order elliptic difference equations. A discussion of iterative techniques and the concept of rate of convergence is given. For various block iteration methods, sufficient conditions were obtained which ensure a higher asymptotic rate of convergence for the cyclically reduced system than for the original system. The use of cyclic reduction in the numerical solution of two-dimensional second-order self-adjoint elliptic differential equations is illustrated. (M.C.G.)

• Research Organization: Westinghouse Electric Corp. Bettis Atomic Power Lab., Pittsburgh
• DOE Contract Number: AT(11-1)-GEN-14
• NSA Number: NSA-16-025691
• OSTI ID: 4812735
• Report Number(s): WAPD-TM-327
• Country of Publication: United States
• Language: English

Related Subjects

DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICS
MATHEMATICS AND COMPUTERS
MATRICES
NUMERICALS