Algorithm 646

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Algorithm 646: PDFIND: a routine to find a positive definite linear combination of two real symmetric matrices

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 12 , Issue 3 (September 1986) table of contents

Pages: 278 - 282

Year of Publication: 1986

ISSN:0098-3500

Author

Charles R. Crawford

York University, 39 MacPherson A.ve., Toronto, Ontario, Canada M5R 1W7

Publisher

ACM New York, NY, USA

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appendices and supplements abstract references index terms collaborative colleagues

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APPENDICES and SUPPLEMENTS

PDFIND (646.gz) (10 KB)

positive definite linear combination of two real symmetric matrices may be used to solve the generalized eigenproblem Ax = (lambda)Bx in case A and B are large and sparse, but neither is positive definite
Gams: D4b1,D4c1c

ABSTRACT

PDFIND is a FORTRAN-77 implementation of an algorithm that finds a positive definite linear combination of two symmetric matrices, or determines that such a combination does not exist. The algorithm is designed to be independent of the data structures used to store the matrices. The user must provide a subroutine, CHLSKY, which acts as an interface between PDFIND and the matrix data structures. CHLSKY also provides the user control over the number of iterations of the algorithm. Implementations of CHLSKY are included which call LINPAC routines for full matrices as well as symmetric banded matrices.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	CRAWFORD, C.R. Bounds for definite matrix pairs. In Proceedings of the 14th Conference on Numerical Mathematics, Congr. Numer. 145 (University of Manitoba, Sept. 27-29, 1984), 59-64.
	2	CRAWFORD, C. R., AND MOON, Y. S. Finding a positive definite linear combination of two Hermitian matrix. Linear Algebra Appl. 51 (19;33), 37-48.
	3	Beresford N. Parlett, The symmetric eigenvalue problem, Prentice-Hall, Inc., Upper Saddle River, NJ, 1998
	4	DONGARRA, J. J., MOLER, C. B., BUNCH, J. R., AND STEWART, G.W. LINPAC User's Guide. SIAM, Philadelphia, Pa., 1979.