However, for the patient reader, the rewards are immense. Parlett has a knack for the perfect footnote—a comment that resolves a subtle confusion or cites an obscure Russian paper that turns out to be crucial. His (e.g., on the origins of the QR algorithm from the LR algorithm) are delightful.
Cornelius Lanczos’s 1950 method for tridiagonalizing a matrix was, for decades, considered unstable due to loss of orthogonality. Parlett, along with his student Jane Cullum and others, rehabilitated the method. The book provides the definitive analysis of and explains why the loss of orthogonality is not a bug but a feature: it signals convergence of the extremal eigenvalues. This insight turned the Lanczos method into the standard for large, sparse symmetric problems. parlett the symmetric eigenvalue problem pdf
: How to use submatrices to find eigenvalue bounds (Cauchy, Weyl, etc.) and Rayleigh-Ritz approximations. SIAM Publications Library Reader's "Survival Guide" The Symmetric Eigenvalue Problem - Beresford N. Parlett However, for the patient reader, the rewards are immense
: Shift to the modern challenge of "large sparse matrices," where the goal is making and judging approximations rather than exact calculations. "Classic" Status : Part of the SIAM Classics in Applied Mathematics This insight turned the Lanczos method into the
Parlett, B. N. (1980). The symmetric eigenvalue problem. Prentice Hall.
