Abstract: "The problem of finding an approximation of x=A[superscript [symbol]]b (where A[superscript [symbol]] is the pseudo-inverse of A [is an element of] R[superscript mxn] with m [is greater than or equal to] n and rank(A)=n) is discussed. It is assumed that A is sparse but has neither a s...

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Sameh, Ahmed (VerfasserIn), Zlatev, Zahari 1939- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Urbana, Ill. 1989
Schriftenreihe:	Center for Supercomputing Research and Development <Urbana, Ill.>: CSRD report 895
Schlagworte:	Linear systems Sparse matrices > Computer programs
Zusammenfassung:	Abstract: "The problem of finding an approximation of x=A[superscript [symbol]]b (where A[superscript [symbol]] is the pseudo-inverse of A [is an element of] R[superscript mxn] with m [is greater than or equal to] n and rank(A)=n) is discussed. It is assumed that A is sparse but has neither a special pattern (as bandedness) nor a special property (as symmetry or positive definiteness). In this paper it is shown that preconditioners obtained by neglecting small elements during the decomposition of A into easily invertible matrices could efficiently be used with gradient-type methods. The preconditioned methods so found are often better than the corresponding direct and pure iterative method Preconditionings in which elements are neglected not because they are small but because they appear at inconvenient places may fail in cases where those obtained by neglecting only small elements succeed (provided that an adaptive strategy for deciding when an element is small is implemented). Numerical results are given to illustrate the performance of preconditioning based on neglecting small elements in connection with conjugate gradient-type methods.
Beschreibung:	11 S.