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Publisher DOI: 10.1137/0612049
Title: A class of arbitrarily ill-conditioned floating-point matrices
Language: English
Authors: Rump, Siegfried M. 
Keywords: condition number;sensitivity;ill-conditioned;linear systems;floating-point number systems
Issue Date: 1991
Source: SIAM J. Matrix Anal. Appl. (SIMAX), 12(4):645-653, 1991
Abstract (english): Let IF be floating-point number system with basis beta > 2 and an exponent range consisting at least of the exponents 1 and 2. A class of arbitrarily ill-conditioned matrices is described the coefficients of which are elements of IF. Due to the very rapidly increasing sensitivity of those matrices they might be regarded as "almost" ill-posed problems. The condition of those matrices and their sensitivity with respect to inversion is given by means of a closed formula. The condition is rapidly increasing with the dimension. E.g. in the double precision of the IEEE 754 floating-point standard (base 2, 53 bits in the mantissa including implicit 1) matrices with 2n rows and columns are given with a condition number of approximately (...)
DOI: 10.15480/882.320
Institute: Zuverlässiges Rechnen E-19 
Type: (wissenschaftlicher) Artikel
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