IMPLEMENTATION OF PARALLEL ONE-SIDED BLOCK JACOBI METHODS FOR THE SYMMETRIC EIGENVALUE PROBLEM
Javier Cuenca, Domingo Giménez · 2000
Introduction The Symmetric Eigenvalue Problem (SEP) can be solved in at least three different ways [10]: 1) methods working by reduction of matrices into certain condensed form, like the QRalgorithm, 2) Jacobi-like methods, and 3) spectral division methods. Jacobi method is the oldest but the interest in Jacobi's approach is renewed due to its inherent parallelism and good stability [3]. Traditional implementations of dense linear algebra algorithms encounter a bottleneck in modern architectures due to limited bandwidth between the CPU and main memory. Using algorithms by blocks, matrix-matrix operations can be arranged so that more computation is performed between memory accesses. As a result, these operations can take advantage of hierarchical memories. A suite of such matrix-matrix operations are part of the basic linear algebra subprograms (BLAS) [4]. An algorithm coded in terms of calls to BLAS becomes a portable high performance implementation. The use of blocks also allo