09-23-2026, 08:25 PM
Matrix Analysis and Computations by Zhong-Zhi Bai and Jian-Yu Pan (2021) is a comprehensive treatment of matrix theory and its applications to numerical computation. The first part develops the mathematical foundations needed for computation, including basic matrix properties, matrix decompositions, numerical ranges, and nonnegative matrices and M-matrices. The second part moves to computational techniques for solving large linear systems, covering matrix-splitting methods, Krylov subspace methods, preconditioning, and saddle-point problems. The book combines rigorous theoretical results with computational perspectives and extensive exercises.
A major theme is how mathematical properties of matrices determine the efficiency and convergence of numerical algorithms. Krylov subspace methods are presented as powerful approaches for large sparse systems, while preconditioning is used to improve their speed and robustness when matrices are ill-conditioned or have unfavorable spectral properties.
The book also addresses saddle-point systems arising in scientific and engineering applications and concludes with practical information about software such as BLAS, LAPACK, MATLAB, and IFISS. Overall, it is designed as both a graduate-level textbook and a reference for researchers working in numerical analysis, optimization, data science, and scientific computing.
BOOK
A major theme is how mathematical properties of matrices determine the efficiency and convergence of numerical algorithms. Krylov subspace methods are presented as powerful approaches for large sparse systems, while preconditioning is used to improve their speed and robustness when matrices are ill-conditioned or have unfavorable spectral properties.
The book also addresses saddle-point systems arising in scientific and engineering applications and concludes with practical information about software such as BLAS, LAPACK, MATLAB, and IFISS. Overall, it is designed as both a graduate-level textbook and a reference for researchers working in numerical analysis, optimization, data science, and scientific computing.
BOOK
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