Fast Algorithms For Some Structured Matrices

Some fast algorithms for certain classes of structured matrices are considered in this thesis. Firstly, we propose several fast algorithms for computing the products of matrix-vector with a generalized centrosymmetric matrix (or generalized centro- hermitian matrix). Secondly, we develop some conventional fast algorithms for computing the products of matrix-matrix with a generalized centrosymmetric matrix (or generalized centrohermitian matrix). At last, we investigate the block algorithms for computing the products of matrix-matrix with a generalized centro- symmetric matrix (or generalized centrohermitian matrix). Comparing with the conventional algorithms, our algorithms ensure significant savings in computational costs and memory units.This paper consists of five chapters.In the first chapter, we mainly introduce the background, the main contents and the originalities of the thesis.In the second chapter, we briefly review some basic definitions and notation which will be used in the thesis.In the third chapter, several algorithms for computing the products of matrix- vector with a centrosymmetric matrix (or a centrohermitian matrix) are proposed. We give some detailed analysis of these algorithms, comparing with the computional costs and storages of the conventional algorithms, our algorithms can save a lot .In the fourth chapter, we offered several conventional fast algorithms for computing the products of matrix-matrix with a generalized centrosymmetric matrix (or a generalized centrohermitian matrix). Those algorithms have the similar savings.In the last chapter, we proposed a few block algorithms for computing the products of matrix-matrix with a generalized centrosymmetric matrix (or a generalized centrohermitian matrix). By using blocked matrix product where some multiplicative operations are transformed into relative additive operations, our algorithms ensure the improvement of computational speed and saving of storage.