Condition number bounds for problems with integer coefficients

Details Condition number bounds for problems with integer coefficients Condition number bounds for problems with integer coefficients

1999-04-22

arxiv.org/abs/math/9904128v1

Journal of Complexity, Volume 16, Issue 3, September 2000, Pages 529-551.

Mathematics

Numerical Analysis

Scientific paper

10.1006/jcom.2000.0552

An apriori bound for the condition number associated to each of the following problems is given: general linear equation solving, minimum squares, non-symmetric eigenvalue problems, solving univariate polynomials, solving systems of multivariate polynomials. It is assumed that the input has integer coefficients and is not on the degenerate locus of the respective problem (i.e. the condition number is finite). Then condition numbers are bounded in terms of the dimension and of the bit-size of the input. In the same setting, bounds are given for the speed of convergence of the following iterative algorithms: QR without shift for the symmetric eigenvalue problem, and Graeffe iteration for univariate polynomials.

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