Parallelizing the Kogbetliantz Method A First Attempt

Date of Online Publication: 14/04/2007
Keywords: singular value decomposition, Kogbetliantz method, parallel algorithm, block algorithm
Authors: Vjeran Hari, Vida Zadelj-Martic
Pages: 49-66
The paper investigates a way how can the two-sided Jacobi-type method for computing the singular value decomposition of triangular matrices, known as Kogbetliantz method, be adapted for use with parallel computers with shared memory. The slower row operations can be replaced, at low extra cost, by the faster column operations. It is shown how can the method be further modified to work with blocks. In any case, the initial triangular or rectangular matrix has to be brought to a special, butter_y-like form. In the iterative part of the algorithm, this special form gradually changes, but after a fixed number of parallel steps, which corresponds to two standard sweeps, the initial butter_y-like form is retained. This property simplifies the algorithm and enhances its performance.

 

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