Review: The Symmetric Eigenvalue Problem by B. N. Parlett

Parlett's Contributions

: Basic facts about self-adjoint matrices, eigenvalue bounds, and counting eigenvalues. Computational Methods : Deflation techniques, Jacobi methods, and Cuppen's divide-and-conquer approach for tridiagonal matrices. Numerical Stability

Depth and Rigor

Parlett doesn’t just list algorithms—he dissects their mathematical foundations. Topics like perturbation theory, Lanczos and Arnoldi processes, and divide-and-conquer methods are treated with precision. The discussion of Krylov subspace methods is especially insightful and still highly relevant.

Also, I want to mention that I couldn't find any direct reference to a PDF of Parlett's book. However, the book is widely available in print and digital formats, and many libraries and online platforms offer access to the book.