论文信息 - Efficient vector and parallel manipulation of tensor products

Efficient vector and parallel manipulation of tensor products

We present efficient vector and parallel methods formanipulating tensor products of matrices. We consider bothcomputing the matrix-vector product (A1Ä¼<fontface="Symbol">ÄAK)x and solving the systemof linear equations (A1Ä¼<fontface="Symbol">ÄAK)x=b. The methods describedare independent of K. We accompany this article with acompanion algorithm which describes an implementation of a completeset of tensor product routines based on LAPACK and the Level 2 and3 Basic Linear Algebra Subprograms (BLAS) which providevectorization and parallelization.

Wayne R. Dyksen | Paul E. Buis

[1] Wayne R. Dyksen. Tensor product generalized ADI methods for separable elliptic problems , 1987 .

[2] Jack J. Dongarra,et al. Algorithm 656: an extended set of basic linear algebra subprograms: model implementation and test programs , 1988, TOMS.

[3] Jack J. Dongarra,et al. A proposal for a set of level 3 basic linear algebra subprograms , 1987, SGNM.

[4] Jack J. Dongarra,et al. A set of level 3 basic linear algebra subprograms , 1990, TOMS.

[5] W. J. Cody,et al. Chebyshev Approximations for the Psi Function , 1973 .

[6] V. Pereyra,et al. Efficient Computer Manipulation of Tensor Products with Applications to Multidimensional Approximation , 1973 .

[7] Jack J. Dongarra,et al. An extended set of FORTRAN basic linear algebra subprograms , 1988, TOMS.

[8] Carl de Boor,et al. Efficient Computer Manipulation of Tensor Products , 1979, TOMS.

[9] E. Grosse. Tensor spline approximation , 1980 .

[10] Wayne R. Dyksen. Tensor Product Generalized ADI Methods for Elliptic Problems , 1984 .