Matrix Computations

The book is about twenty-five percent longer. There are new sections on fast transforms ( § 1 .4), parallel LU (§3.6), fast methods for circulant systems and discrete Poisson systems ( §4.8) , Hamiltonian and product eigenvalue problems (§7.8) , pseudospectra (§7.9) , the matrix sign, square root, and logarithm functions (§9.4) , Lanczos and quadrature (§10.2), large-scale SVD (§ 10.4) , Jacobi-Davidson (§ 10.6) , sparse direct methods ( § 1 1 . 1 ) , multigrid ( § 1 1 .6) , low displacement rank systems ( § 12. 1 ) , structuredrank systems ( § 12.2) , Kronecker product problems (§12.3), tensor contractions ( § 12 .4) , and tensor decompositions ( § 12.5) . New topics at the subsection level include recursive block LU (§3.2 . 1 1 ) , rook pivoting (§3.4.7) , tournament pivoting (§3.6.3), diagonal dominance (§4. 1 . 1 ) , recursive block structures (§4.2. 10), band matrix inverse properties (§4.3.8) , divide-and-conquer strategies for block tridiagonal systems (§4.5.4) , the cross product and various point/plane least squares problems ( §5.3.9) , the polynomial eigenvalue problem (§7.7.9) , and the structured quadratic eigenvalue problem (§8. 7.9) . Substantial upgrades include our treatment of floating-point arithmetic (§2.7) , LU roundoff error analysis (§3.3. 1 ) , LS sensitivity analysis (§5.3.6) , the generalized singular value decomposition (§6. 1 . 6 and §8.7.4) , and the CS decomposition (§8.7.6) .