Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations (Classic Reprint) - Hardcover
Synopsis
Understand how finite-precision math affects Lanczos and CG methods in this focused study of numerical linear algebra.
See how rounding errors can shape eigenvalue approximations and convergence behavior, with clear comparisons to exact results.
This edition analyzes how finite precision computations mimic or diverge from ideal algorithms, using practical examples and visual evidence. It highlights when and why errors alter convergence rates, and what that means for solving large linear systems and eigenvalue problems.- How rounding affects eigenvalue estimates in Lanczos iterations
- Conditions under which finite-precision CG matches or diverges from exact results
- Illustrative figures showing the relationship between finite and exact computations
- Discussion of bounds, interval widths, and open questions in this area
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