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Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in the right hand side
Jansson C. Computing46 (3):265-274,1991.Type:Article
Date Reviewed: Jun 1 1993

This well-written paper deals with computing bounds on the solution sets of linear systems of equations A x = b in which there is uncertainty in the coefficients and right-hand sides, and in which the matrices are symmetric or skew-symmetric, or in which the components of the right-hand vector are related through formulas. The machinery used, interval analysis, is not belabored, but ample pointers to introductions are given for nonexperts. The main formulas, related to those of S. M. Rump, lead to a computational algorithm that gives rigorous bounds on the set of possible solutions as well as rigorous estimates on how sharp these bounds are. (That is, inner and outer solutions are computed.) The technique takes advantage of the symmetry to give tighter bounds than an algorithm that assumes that the matrix elements vary entirely arbitrarily. Jansson separately outlines a technique and proves a theorem on how to take advantage of dependencies in the right-hand vector b . Jansson gives two numerical examples, which he computed using the programming language CALCULUS.

Reviewer:  Baker Kearfott Review #: CR116202
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Linear Systems (Direct And Iterative Methods) (G.1.3 ... )
 
 
Computations On Matrices (F.2.1 ... )
 
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