Families of algorithms related to the inversion of a Symmetric Positive Definite matrix

We present families of algorithms for operations related to the computation of the inverse of a Symmetric Positive Definite (SPD) matrix: Cholesky factorization, inversion of a triangular matrix, multiplication of a triangular matrix by its transpose, and one-sweep inversion of an SPD matrix. These algorithms are systematically derived and implemented via the Formal Linear Algebra Methodology Environment (FLAME), an approach for developing linear algebra algorithms. How different members of these families of algorithms are more or less suited for a given architecture is demonstrated via implementations for sequential, shared-memory, and distributed memory parallel architectures. Performance on various platforms is reported.

• Type: Journal
• Year: 2008
• Where: TOMS
• Authors: Paolo Bientinesi, Brian C. Gunter, Robert A. van de Geijn
• Keywords: Algorithms, Linear Algebra, TOMS 2008, Triangular Matrix