منابع مشابه
Fast matrix multiplication is stable
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63–72]. As a consequence of our analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also s...
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متن کاملFast linear algebra is stable
In [23] we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of n-by-n matrices can be done by any algorithm in O(n) operations for any η > 0, then it can be done stably in O(n) operations for any η > 0. Here we extend this result to show that essentially all standard linear algebra operations, includin...
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In their seminal work on the Stable Marriage Problem, Gale and Shapley [3] describe an algorithm which finds a stable marriage in O(n) communication rounds. Their algorithm has a natural interpretation as a distributed algorithm where each player is represented by a single processor. The complexity measure of such a distributed algorithm is typically measured by the round complexity, assuming a...
متن کاملFast and Stable Unitary Qr Algorithm
A fast Fortran implementation of a variant of Gragg’s unitary Hessenberg QR algorithm is presented. It is proved, moreover, that all QRand QZ-like algorithms for the unitary eigenvalue problems are equivalent. The algorithm is backward stable. Numerical experiments are presented that confirm the backward stability and compare the speed and accuracy of this algorithm with other methods.
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ژورنال
عنوان ژورنال: The Journal of Organic Chemistry
سال: 2006
ISSN: 0022-3263,1520-6904
DOI: 10.1021/jo060921d