Matrix Analysis and Computations

The book is organized into two sections. The first lays out the foundations of matrix analysis that later computational work depends on. The second turns to representative computational methods and the theory behind them. Each chapter ends with a substantial set of exercises.

The central aim is to supply the matrix theory needed for matrix computation, especially direct and iterative techniques for solving systems of linear equations. A large part of the coverage is devoted to matrix splitting iteration and Krylov subspace iteration, developed systematically and with rigorous theory. The book also reports recent results on preconditioning and on iterative methods for standard and generalized saddle-point linear systems.

It is written to serve as a graduate textbook and also works as a self-study guide and reference for researchers and engineers working in matrix analysis and computation. It suits courses in numerical analysis, numerical optimization, data science, and approximation theory, among other subjects.