Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature-everything needed to become a matrix-savvy developer of numerical methods and software. The proper organization of the matrix computations is becoming more and more important when high-speed computers with hierarchical memory (based on several levels of caches) are used in the treatment of large computational tasks. Matrix computations are used in the treatment of nearly all large-scale models. Applications of matrices are found in most scientific fields. In every branch of physics, including classical mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, they are used to study physical phenomena, such as the motion of rigid bodies. In computer graphics, they are used to manipulate 3D models and project them onto a 2-dimensional screen. In probability theory and statistics, stochastic matrices are used to describe sets of probabilities; for instance, they are used within the PageRank algorithm that ranks the pages in a Google search. Matrix calculus generalizes classical analytical notions such as derivatives and exponentials to higher dimensions. Matrices are used in economics to describe systems of economic relationships. This book is thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process.