Analytical Modeling of Matrix-Vector Multiplication on Multicore Processors: Solving Inverse Gravimetry Problem
Elena Nikolaevna Akimova, Roman A. Gareev, Vladimir Evgenevich Misilov · 2019 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON) · 2019
Effective implementation of matrix-vector multiplication is of considerable practical significance. Current methods cannot automatically optimize it sufficiently under severe constraints of compilation time. All major existing approaches require optimized external code. We introduce a compiler transformation, which is used for automatic optimization of the matrix-vector multiplication. The optimization is based on modeling of the computations on the hypothetical processor and, therefore, can be used without access to the target platform and when the execution time is a critical factor. As an example of practical application of the approach, we consider implementation of a solution of the inverse gravimetry problem of finding an interface between the layers using the iterative Levenberg-Marquardt method. Through the approximation, we reduce the problem to an ill-conditioned system of linear equations with the matrix, which is defined as multiplication of the original matrix and its transposition. We apply the presented algorithm to optimize our implementation on multicore processors. We show that our approach is competitive with the expert-tuned libraries.