Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) / Gene H. Golub, Charles F. Van Loan

The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool.

This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on
fast transforms
parallel LU
discrete Poisson solvers
pseudospectra
structured linear equation problems
structured eigenvalue problems
large-scale SVD methods
polynomial eigenvalue problems

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 second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.