A method of virtual displacements for the degenerate discrete approximation problem

Authors:
W. Fraser and J. M. Bennett

Journal:
Math. Comp. **32** (1978), 421-430

MSC:
Primary 41A50

DOI:
https://doi.org/10.1090/S0025-5718-1978-0487191-8

MathSciNet review:
0487191

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Abstract | References | Similar Articles | Additional Information

Abstract: Given the system of equations

*X*which provides a minimum of

*k*values of the index

*i*. If for exactly

*k*values of the index

*i*, the point or vertex is called ordinary, while if for more than

*k*values of

*i*, the vertex is termed degenerate.

A necessary and sufficient condition to determine if *X* minimizes *R* is valid if *X* is an ordinary vertex but not if *X* is degenerate. A degeneracy at *X* can be removed by applying perturbations to an appropriate number of the so that *X* becomes an ordinary vertex of a modified problem. By noting that the test uses only values of the , it is possible to avoid actual introduction of the perturbations to the with a resulting substantial improvement of the efficiency of the computation.

**[1]**I. BARRODALE & F. D. K. ROBERTS, "Solution of an overdetermined system of equations in the norm,"*Comm. ACM*, v. 17, 1974.

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0487191-8

Article copyright:
© Copyright 1978
American Mathematical Society