Compiled in this book is a selection of articles written by internationally recognized experts in the fields of matrix computation and signal processing. In almost all digital signal processing (DSR) problems, the available data is corrupted by (measurement) noise or is incomplete. Classical techniques are unable to separate ''signal'' spaces and ''noise'' spaces. However, the information hidden in the data can be made explicit through singular value decomposition (SVD). SVD based signal processing is making headway and will become feasible soon, thanks to the progress in parallel computations and VLSI implementation. The book is divided into six parts. Part one is a tutorial, beginning with an introduction, including (VLSI) parallel algorithms and some intriguing problems. It describes several applications of SVD in system identification and signal detection. It also deals with the fundamental harmonic retrieval problem and principal component analysis. Part two discusses details of model reduction, system identification and detection of multiple sinusoids in white noise, while part three is devoted to the total-least-squares and generalized singular value decomposition problems. The fourth section deals with real-time and adaptive algorithms, the fifth examines fast algorithms and architectures, such as block-algorithms, computational arrays, systolic arrays, hypercubes and connection machines, and the final part addresses some open problems.