Parallel Triangular Sylvester-Type Matrix Equation Solvers for SMP Systems Using Recursive Blocking [chapter]

Isak Jonsson, Bo Kågström
2001 Lecture Notes in Computer Science  
We present recursive blocked algorithms for solving triangular Sylvester-type matrix equations. Recursion leads to automatic blocking that is variable and \squarish". The main part of the computations are performed as level 3 general matrix multiply and add (GEMM) operations. We also present new highly optimized superscalar kernels for solving small-sized matrix equations stored in level 1 cache. Hereby, a larger part of the total execution time will be spent in GEMM operations. In turn, this
more » ... ads to much better performance, especially for small to medium-sized problems, and improved parallel scalability on shared memory processor (SMP) systems. Uniprocessor and SMP parallel performance results are presented and compared with results from existing LAPACK routines for solving this type of matrix equations.
doi:10.1007/3-540-70734-4_10 fatcat:g6pdbwihxbbe5a3amazqrh7a7y