The Matrix Computation Toolbox is a collection of MATLAB M-files containing functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search optimization. Various other miscellaneous functions are also included.

This toolbox supersedes the Test Matrix Toolbox [606, 1995] that was described in the first edition of this book. Most of the test matrices in that toolbox have been incorporated into MATLAB in the gallery function. The new toolbox incorporates some of the other routines in the Test Matrix Toolbox and adds several new ones.

Of particular relevance to this book are functions for

• Cholesky factorization with complete pivoting for a symmetric positive semidefinite matrix: cholp;

• rounding matrix elements to a specified number of bits-useful for simulating lower precision in experiments: chop;

• GE with one of four optional pivoting strategies: no pivoting, partial pivoting, rook pivoting, and complete pivoting: gep;

• Gauss-Jordan elimination with no pivoting or partial pivoting for solving a linear system: gj;

• generalized QR factorization: gqr;

• the classical and modified Gram-Schmidt methods for QR factorization: gs_c, gs_m;

• block LDL ^T factorization of symmetric matrices with partial pivoting or rook pivoting: 1dlt_symm;

• block LDL ^T factorization of symmetric tridiagonal matrices with Bunch's pivoting strategy: 1dlt_sytr;

• block LDL ^T factorization of skew-symmetric matrices with Bunch's partial pivoting strategy: 1dlt_skew;

• solving the equality constrained least squares problem: 1se;

• two- and three-dimensional views of pseudospectra: ps, pscont;

• direct search optimization by the alternating...