High Performance Scalable Recursive Block Matrix Inverse for Multicore Architectures

The inversion of a matrix, which is computationally intensive and involves numerous operations, is extensively used in various scientific and engineering applications. The block matrix inverse formula for n x n matrices requires the inverse of two half-sized matrices and six multiplications between two half-sized matrices. In this work, we proposed high performance scalable recursive block matrix inverse algorithm for multicore architectures based on block matrix inverse that performs recursively and transforms two half-sized matrices into a minimal 2 x 2 matrix inverse. We performed extensive experimental performance evaluation and analysis of recursive block matrix inverse on shared memory multicore system and achieved scalability and throughput (Double Precision GFLOPS) for large matrix inversion. We compared recursive block matrix inverse with MKL LAPACK and found it to be far superior. We proposed a combination of recursive block matrix inverse and MKL LAPACK matrix multiplication routines for multicore architectures, which outperforms MKL LAPACK matrix inverse.