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The orthogonal qd-algorithm. (English) Zbl 0895.65014
The paper presents an algorithm to compute the singular values and the singular vectors of a square bidiagonal matrix. This algorithm uses the differential form of the generalized Givens transformation to compute the orthogonal \(qd\)-steps, and two different shift strategies based on Newton’s and Laguerre’s methods to compute the zeros of a polynomial. Finally, some numerical results are given.

MSC:
65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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