A Structured Orthogonal Inversion of Block p-cyclic Matrices on Multicores with GPU Accelerators

Block p-cyclic matrices is an important class of block structured matrices with broad applications in numerical analysis of differential equations, Markov chains theory, computational quantum chem-istry and beyond. We present a method for structured orthogonal inversion of p-cyclic matrices with a set of algorithmic improvements for gaining better performance on multicores with GPU accelerators. Benchmarking has shown that our codes for hybrid CPU+GPU systems maintain relatively sustainable performance for different values of parameter n, and attain up to 90 % of peak performance with suf-ficiently large matrices. The solutions proposed here can be easily extended to the target architectures with multiple GPUs, and to the problems with more general block structured matrices. Keywords: block p-cyclic matrix, matrix inversion, structured orthogonal factorization, block back substitution, Householder QR factorization, load balancing, GPU ac-celerated linear algebra