منابع مشابه
Backward Error Analysis for Totally Positive Linear Systems
Gauss elimination applied to an n • n matrix ,4 in floating point arithmetic produces (if successful) a factorization /-U which differs from A by no more than ~ ILl ] U I, for some ~ of order n times the unit roundoff. If A is totally positive, then both computed factors /~ and U are nonnegative for sufficiently small unit roundoff and one obtains pleasantly small bounds for the perturbation in...
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Every nonsingular totally positive m-banded matrix is shown to be the product of m totally positive one-banded matrices and, therefore, the limit of strictly m-banded totally positive matrices. This result is then extended to (bi)infinite m-banded totally positive matrices with linearly independent rows and columns. In the process, such matrices are shown to possess at least one diagonal whose ...
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We study asymptotic behavior of solutions of general advanced differential systems y(t) = F(t, y(t)), where F : Ω → [Symbol: see text] (n) is a continuous quasi-bounded functional which satisfies a local Lipschitz condition with respect to the second argument and Ω is a subset in [Symbol: see text] × C(r)(n), C(r)(n) := C([0, r], [Symbol: see text] (n)), y t [Symbol: see text]C(r)(n), and y t (...
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This paper simplifies and generalizes an earlier result of the author's on Gauss interpolation formulas for the one-dimensional heat equation. Such formulas approximate a function at a point (x*, t*) in terms of a linear combination of its values on an initial-boundary curve in the (x, t) plane. The formulas are characterized by the requirement that they be exact for as many basis functions as ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1970
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1970.32.203