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A fully parallel algorithm for the symmetric eigenvalue problem. (English) Zbl 0627.65033

Let A be a real symmetric matrix. Solving the eigenvalue problem means to determine an orthogonal matrix Q and a diagonal matrix D such that \(A=QDQ^ T\). The way the paper provides for solving the problem consists of two steps. The first transforms A to a tridiagonal symmetric matrix T. Here, a Householder reduction is used which is also qualified for a parallel computation. The second step, which is the primary purpose of the paper, is the decomposition of the above transformation (with T instead of A) into two smaller parts, which are then ready for parallel processing. The decomposition is based upon a combination of a divide and conquer technique by J. J. M. Cuppen [Numer. Math. 36, 177-195 (1981; Zbl 0431.65022)] and on a rank-one updating of the eigensystem of symmetric matrices due to J. R. Bunch, C. P. Nielsen and the second author [ibid. 31, 31-48 (1978; Zbl 0369.65007)] and G. H. Golub [SIAM Rev. 15, 318-334 (1973; Zbl 0227.65025)].
Reviewer: H.Ratschek

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65Y05 Parallel numerical computation

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