CACHE-OPTIMIZATION OF SOLVING EIGENVALUES PROBLEM FOR PARALLEL COMPUTING SYSTEMS
The reduction of the matrix to Hessenberg form in the framework of the problem of calculating eigenvalues on parallel computing systems with shared memory is considered. Parallel computing systems with shared memory are the most common and affordable type of parallel computing systems. As the base conversion use the conversion reflections of Householder. The article analyzes the solution of the problem of reducing the matrix to Hessenberg form on the target computing architectures, with special attention paid to the optimization of algorithms in terms of efficient use of cache memory. The author's algorithms for solving the problem, which are optimized versions of the classical householder transformation, are presented. The use of these algorithms can significantly reduce the execution time of the program. The conclusions are confirmed by the results of computational experiments.