A method of virtual displacements for the degenerate discrete approximation problem
W. Fraser and J. M. Bennett
Math. Comp. 32 (1978), 421-430
Full-text PDF Free Access
Similar Articles |
Abstract: Given the system of equations let . It is known that if the matrix has rank , then there is a point X which provides a minimum of such that for at least 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.
I. BARRODALE & F. D. K. ROBERTS, "Solution of an overdetermined system of equations in the norm," Comm. ACM, v. 17, 1974.
- I. BARRODALE & F. D. K. ROBERTS, "Solution of an overdetermined system of equations in the norm," Comm. ACM, v. 17, 1974.
Retrieve articles in Mathematics of Computation
Retrieve articles in all journals
© Copyright 1978
American Mathematical Society