Synopsis
Master the math behind fast linear solvers.
This clear guide explains how conjugate gradient methods work through a variational lens, linking ideas like Krylov subspaces, Lanczos vectors, and preconditioning to practical algorithms.
In accessible chapters, you’ll see how to turn a linear system into efficient iterative steps, understand when methods converge, and learn how special cases (symmetric, nonsymmetric, indefinite) change the approach. The text ties theory to algorithm design, showing how error bounds arise from polynomial approximation and how stable implementations like SYMMLQ and MINRES are constructed.- How Krylov subspaces are built and why Lanczos recurrences matter
- Variational foundations that lead to stable, efficient solvers
- Different problem types (symmetric, nonsymmetric, positive definite) and their implications
- Preconditioning ideas to improve convergence without changing the solution
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