Efficient Parallel Algorithm for Constructing a Unit Triangular Matrix with Prescribed Singular Values
Georgina Flores-Becerra (Instituto Tecnologico de Puebla)Victor M. Garcia (Universidad Politecnica de Valencia)
Antonio M. Vidal (Universidad Politecnica de Valencia)
Abstract:
The problem tackled in this paper is the parallel construction of a unit triangular matrix with prescribed singular values, when these fulfill Weyl's conditions [1]; this is a particular case of the Inverse Singular Value Problem. A sequential algorithm for this problem was proposed in [2] by Kosowsky and Smoktunowicz. In this paper parallel versions of this algorithm will be described, both for shared memory and distributed memory architectures. The proposed parallel implementation is better suited for the shared memory paradigm; this is confirmed by the numerical experiments; the shared memory version, reaches an efficiency over 90%, and reduces substantially the execution times compared with the sequential algorithm.
[1] Horn A.: On the eigenvalues of a matrix with prescribed singular values. Proc. Amer. Math. Soc., Vol.5, (1954) 4-7
[2] Kosowski P., Smoktunowicz A.: On Constructing Unit Triangular Matrices with Prescribed Singular Values. Computing, Vol.64, No.3 (2000) 279-285
Keywords:
Numerical Methods (Linear algebra), Numerical Methods (Non-Linear algebra), Parallel and Distributed Computing
