A fully portable high performance minimal storage hybrid format Cholesky algorithm
Copyright policy )A fully portable high performance minimal storage hybrid format Cholesky algorithm
We consider the efficient implementation of the Cholesky solution of symmetric positive-definite dense linear systems of equations using packed storage. We take the same starting point as that of LINPACK and LAPACK, with the upper (or lower) triangular part of the matrix stored by columns. Following LINPACK and LAPACK, we overwrite the given matrix by its Cholesky factor. We consider the use of a hybrid format in which blocks of the matrices are held contiguously and compare this to the present LAPACK code. Code based on this format has the storage advantages of the present code but substantially outperforms it. Furthermore, it compares favorably to using conventional full format (LAPACK) and using the recursive format of Andersen et al. [2001].
- Technical University of Denmark Denmark
- Rutherford Appleton Laboratory United Kingdom
- IBM (United States) United States
- Science and Technology Facilities Council United Kingdom
- Danish Meteorological Institute Denmark
Complexity and performance of numerical algorithms, LAPACK, Packaged methods for numerical algorithms, Direct numerical methods for linear systems and matrix inversion, LINPACK, symmetric positive-definite dense systems, Cholesky factorization
Complexity and performance of numerical algorithms, LAPACK, Packaged methods for numerical algorithms, Direct numerical methods for linear systems and matrix inversion, LINPACK, symmetric positive-definite dense systems, Cholesky factorization
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