The recent availability of advanced architecture computers has had a very sigificant impact on all spheres of scientific computation including algorithm research and software development in numerical linear algebra. Major elements of these new computers and recent developments in linear equation algorithms for dense and sparse matrices that are designed to exploit these elements are discussed here. Many techniques and current understandings about solving systems of linear equations on vector and shared-memory parallel computers are documented and unified, providing a fast entrance to the world of vector and parallel processing for these linear algebra applications. This book is both a reference and a supplemental teaching text on aspects of scientific computation for use by graduate students, researchers working in computational science, and numerical analysts.