A Mean Square Estimate of the Generated Roundoff Error in Constant Matrix Iterative Processes

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A Mean Square Estimate of the Generated Roundoff Error in Constant Matrix Iterative Processes

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Journal of the ACM (JACM) archive
Volume 18 , Issue 1 (January 1971) table of contents

Pages: 48 - 62

Year of Publication: 1971

ISSN:0004-5411

Authors

N. F. Benschop	University of Waterloo, Department of Electrical Engineering, Waterloo, Ontario, Canada
H. C. Ratz	University of Waterloo, Department of Electrical Engineering, Waterloo, Ontario, Canada

Publisher

ACM New York, NY, USA

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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	VAROA, R.S. Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, N.J., 1962.
	2	OSTROWSKI, A.M. Solution of Equations and Systems of Equations. Academic Press, New York, 1966, pp. 30, 251.
	3	FXDDEEV, D. K., AND FADDEEVA, V.N. Computational Methods of Linear Algebra. W. H. Freeman and Co., San Francisco, Calif., 1963.
	4	YON NEUMANN, Z., AND GOLDSTINE, H.H. Numerical inverting of matrices of high order: Pt. I, Bull. Amer. Math. Soc. 53 (1947), 1021-1099; Pt. II, Proc. Amer. Math. Soc. 2 (1951), 188-202.
	5	KLYUYEV, V. V., AND KOKOVKIN-SHCHERBAK, N .I . On the minimization of the number of arithmetic operations for the solution of linear algebraic systems of equations. Teeh. Rep. CS 24, Comput. Sci. Dep., Stanford U., Stanford, Calif., June 1965.
	6	STRASSEN, V. Gaussian elimination not optimal. Numer. Math. 13, 4 (Aug. 1969), 354-356.
	7	ROSANOFF, R.A. A survey of modern nonsense asapplied to matrix calculus. Proc. ASME/ AIAA 10th Structures, Structural Dynamics and Materials Conference, New Orleans, La., April 14-16, 1969, pp. 275-284.
	8	TVRINO, A.M. Rounding off errors in matrix processes. Quart. J. Mech. Appl. Math. I (1948), 287-308.
	9	ALBASINY, E.L. Error in digital solution of linear problems. In Error in Digital Computation, Vol. 1, L. B. Rall, Ed., Wiley, New York, 1965, pp. 137-184.
	10	HENRICI, P. Bounds of iterates, inverses, spectral variation and fields of values of nonnormal matrices. Numer. Math. ~ (1962), 24-40.
	11	James H. Wilkinson, Rounding Errors in Algebraic Processes, Dover Publications, Incorporated, 1994
	12	LANCZOS, C. Applied Analysis. Prentice-Hall, Englewood Cliffs, N.J., 1956, pp. 167-206.
	13	URABE, M. Roundoff error distribution in fixed-point multiplication and a remark about the rounding rule. SIAM J. Numer. Anal. 5, 2 (June 1968), 202-210.
	14	HOUSEHOLDER, A.S. Principles o~ Numerical Analysis. McGraw-Hill, New York, 1953, p. 147.
	15	Donald E. Knuth, The Art of Computer Programming Volumes 1-3 Boxed Set, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1998