ISSN:
1436-4646
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Some theorems are given which relate to approximating and establishing the existence of solutions to systemsF(x) = y ofn equations inn unknowns, for variousy, in a region of euclideann-space E n . They generalize known theorems. Viewing complementarity problems and fixed-point problems as examples, known results or generalizations of known results are obtained. A familiar use is made of homotopies H: E n × [0, 1]→E n of the formH(x, t) = (1 −t)F 0 (x) + t[F(x) − y] where theF 0 in this paper is taken to be linear. Simplicial subdivisionsT k of E n × [0, 1] furnish piecewise linear approximatesG k toH. The basic computation is via the generation of piecewise linear curvesP k which satisfyG k (x, t) = 0. Visualizing a sequence {T k } of such subdivisions, with mesh size going to zero, arguments are made on connected, compact limiting curvesP on whichH(x, t) = 0. This paper builds upon and continues recent work of C.B. Garcia.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01593801
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