A block multirate paradigm for efficient parallel algorithm development

A new multirate paradigm is introduced. Multirate signal procesing is shown to be a powerful divide and conquer methodology capable of being applied to the entire field of numerical linear algebra. Multirate can be successfully applied to vector-vector, matrix-vector, and matrix-matrix operations. These operations form the foundation of such software suites as LAPACK. Since LAPACK is dependent upon BLAS, and BLAS is, in turn, dependent upon these three operations, it can be seen that multirate can be applied to problems encountered throughout the field of numerical linear algebra. As an example of practical numerical linear algebra problems (which happen to be encountered in signal processing), the new paradigm for multirate is applied to the FFT. In the case of the FFT, multirate provides an alternate means of generating the four step FFT reported by Van Loan (1992) for use in MIMD shared memory architectures. Thus, multirate can be applied to traditionally sequential algorithms to improve their performance.