09-23-2026, 05:27 PM
Computational Matrix Analysis by Alan J. Laub is a compact introduction to numerical linear algebra focused on how matrix algorithms actually behave on computers. Rather than treating matrices purely theoretically, the book emphasizes finite-precision arithmetic, rounding errors, conditioning, numerical stability, and computational cost. It develops the practical foundations needed to solve linear systems, covering floating-point computation, numerical matrix operations, Gaussian elimination, perturbation and error analysis, and techniques for estimating the sensitivity of computed solutions.
The second half moves to important computational matrix problems: linear least squares and QR factorization, eigenvalue and eigenvector computation, singular-value decomposition, and generalized eigenvalue problems. The final chapter connects these techniques with applications involving matrix functions—especially the matrix exponential—and Lyapunov, Sylvester, and Riccati equations arising in control and systems theory.
Overall, the book is designed as a bridge between theoretical matrix analysis and reliable numerical computation, explaining not only which algorithms work, but also why they work, when they can fail, and how accurately their results can be trusted.
BOOK
The second half moves to important computational matrix problems: linear least squares and QR factorization, eigenvalue and eigenvector computation, singular-value decomposition, and generalized eigenvalue problems. The final chapter connects these techniques with applications involving matrix functions—especially the matrix exponential—and Lyapunov, Sylvester, and Riccati equations arising in control and systems theory.
Overall, the book is designed as a bridge between theoretical matrix analysis and reliable numerical computation, explaining not only which algorithms work, but also why they work, when they can fail, and how accurately their results can be trusted.
BOOK
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