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A class of arbitrarily ill-conditioned floating-point matrices
Citation Link: https://doi.org/10.15480/882.320
Publikationstyp
Journal Article
Date Issued
1991
Sprache
English
Author(s)
Institut
TORE-DOI
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 (...)
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 (...)
Subjects
condition number
sensitivity
ill-conditioned
linear systems
floating-point number systems
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