A recursive formulation of the inversion of symmetric positive definite matrices in packed storage data format

Abstract

A new Recursive Packed Inverse Calculation Algorithm for symmetric positive definite matrices has been developed. The new Recursive Inverse Calculation algorithm uses minimal storage, n(n + 1)/2, and has nearly the same performance as the LAPACK full storage algorithm using n2 memory words. New recursive packed BLAS needed for this algorithm have been developed too. Two transformation routines, from the LAPACK packed storage data format to the recursive storage data format were added to the package too. We present performance measurements on several current architectures that demonstrate improvements over the traditional packed routines.