Randomization and the parallel solution of linear algebra problems

被引：0
|
作者：
Del Corso, G.M. [1 ]
机构：
[1] Instituto di Matematica, Computazionale, Pisa, Italy
来源：
Computers and Mathematics with Applications | 1995年 / 30卷 / 11期
关键词：
Approximation theory - Chebyshev approximation - Computational complexity - Computer simulation - Eigenvalues and eigenfunctions - Linear algebra - Matrix algebra - Parallel processing systems - Probability - Problem solving - Random access storage - Random processes;
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摘要：
We present randomized algorithms for the solution of some numerical linear algebra problems. The problems studied are the approximation of the dominant eigenvalue of a matrix, the computation of the determinant and of the rank of a matrix. The parallel cost of these methods is lower than that of the best deterministic algorithms for the same problems. In particular we show an O(log n) algorithm for the parallel computation of the determinant of a matrix and an O(log n + log k) algorithm that allows to approximate the vector produced at the kth step of the power method. The 'probabilistic' error is bounded in terms of the Chebyshev inequality.
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页码：59 / 72
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