A class of arbitrarily ill-conditioned floating-point matrices

Rump, Siegfried M.Siegfried M.Rump2008-04-092008-04-091991SIAM J. Matrix Anal. Appl. (SIMAX), 12(4):645-653, 1991http://tubdok.tub.tuhh.de/handle/11420/322Let 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 (...)enhttp://doku.b.tu-harburg.de/doku/lic_ohne_pod.phpcondition numbersensitivityill-conditionedlinear systemsfloating-point number systemsA class of arbitrarily ill-conditioned floating-point matricesJournal Articleurn:nbn:de:gbv:830-tubdok-393210.15480/882.32011420/32210.1137/061204910.15480/882.320930767730Journal Article