the purpose of this book is to unify and document in one place many of the techniques and much of the current understanding about solving systems of linear equations on vector and parallel computers. this book is not a textbook,but it is meant to provide a fast entrance to the world of vector and parallel processing for these linear algebra applications. we intend this book to be used by three groups of readers: graduate students, researchers working in computational science, and numerical analysts. as such, we hope this book can serve both as a reference and as a supplement to a teaching text on aspects of scientific computation. the book is divided into five major parts: (1) introduction to terms and concepts, including an overview of the state of the art for high-performance computers and a discussion of performance evaluation (chapters 1-4); (2) direct solution of dense matrix problems (chapter 5); (3) direct solution of sparse systems of equations (chapter 6); (4) iterative solution of sparse systems of equations (chapters 7-9); and (5) iterative solution of sparse eigenvalue problems (chapters 10-11). any book that attempts to cover these topics must necessarily be somewhat out of date before it appears, because the area is in a state of flux. we have purposely avoided highly detailed descriptions of popular machines and have tried instead to focus on concepts as much as possible; nevertheless, to make the description more concrete, we do point to specific computers.