Paa2 Deliverable Apparc Esprit Contract a Strassen-type Matrix Inversion Algorithm

Deliverable for ESPRIT BRA APPARC Algorithms for Data Locality Optimization

Triangular Factorization and Inversion by Fast Matrix Multiplication

The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of ordern in <Cxnlos'7 operations, and, hence, the inverse of any nonsingular matrix in <Cürtlog'7 operations.

Lectures 1 and 2 Matrix Multiplication and Matrix Inversion 1 Prior Work on Matrix Multiplication

There has been much effort to improve the runtime of matrix multiplication. The trivial algorithm multiplies n×n matrices in O(n) time. Strassen (’69) surprised everyone by giving an O(n) time algorithm. This began a long line of improvements until in 1986, Coppersmith and Winograd achieved O(n). After 24 years of no progress, in 2010 Andrew Stothers, a graduate student in Edinburgh, improved t...

Laderman matrix multiplication algorithm can be constructed using Strassen algorithm and related tensor's isotropies

In 1969, V. Strassen improves the classical~2x2 matrix multiplication algorithm. The current upper bound for 3x3 matrix multiplication was reached by J.B. Laderman in 1976. This note presents a geometric relationship between Strassen and Laderman algorithms. By doing so, we retrieve a geometric formulation of results very similar to those presented by O. Sykora in 1977.

Exascale Ready Work-Optimal Matrix Inversion

In this thesis I present a new algorithm OPT for matrix inversion that builds on a matrix multiplication subroutine. It is combined of Strassen’s matrix inversion algorithm and Newton approximation. OPT overcomes the linear lower bound in parallel runtime of Strassen’s inversion algorithm and traditional Gaussian elimination without the log-factor more work of Newton approximation. In particula...