A comment on the Eispack machine epsilon routine

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A comment on the Eispack machine epsilon routine

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ACM SIGNUM Newsletter archive
Volume 28 , Issue 4 (October 1993) table of contents

Pages: 2 - 6

Year of Publication: 1993

ISSN:0163-5778

Authors

Tim Hopkins
John Slater

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 7, Downloads (12 Months): 17, Citation Count: 2

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ABSTRACT

We analyze the algorithm used to generate the value for the machine epsilon in the Eispack suite of routines and show that it can fail on a binary floating-point system. The comments in the code describing the conditions under which this method will work are not restrictive enough and we provide a replacement set of assumptions. We conclude by suggesting how the algorithm may be modified to overcome most of the shortcomings.

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	W. J. Cody, Algorithm 665: Machar: a subroutine to dynamically determined machine parameters, ACM Transactions on Mathematical Software (TOMS), v.14 n.4, p.303-311, Dec. 1988 [doi>10.1145/50063.51907]
	2	B. S. Garbow, J. M. Boyle, J. J. Dongarra, and C. B. Moler. <i>Matrix Eigensystem Routines: EISPACK Guide Extensions.</i> Volume 51 of <i>Lecture Notes in Computer Science</i>, Springer-Verlag, Berlin, 1977.
	3	W. Morven Gentleman , Scott B. Marovich, More on algorithms that reveal properties of floating point arithmetic units, Communications of the ACM, v.17 n.5, p.276-277, May 1974 [doi>10.1145/360980.361003]
	4	Michael A. Malcolm, Algorithms to reveal properties of floating-point arithmetic, Communications of the ACM, v.15 n.11, p.949-951, Nov. 1972 [doi>10.1145/355606.361870]
	5	B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema, and C. B. Moler. <i>Matrix Eigensystem Routines: EISPACK Guide.</i> Volume 6 of <i>Lecture Notes in Computer Science</i>, Springer-Verlag, Berlin, 1976.

CITED BY 2

	Tim Hopkins, Remark on algorithm 705: A Fortran-77 software package for solving the Sylvester matrix equation AXB^T + CXD^T = E, ACM Transactions on Mathematical Software (TOMS), v.28 n.3, p.372-375, September 2002
	Tim Hopkins, Renovating the collected algorithms from ACM, ACM Transactions on Mathematical Software (TOMS), v.28 n.1, p.59-74, March 2002