Tag
krylov-methods
- Oct 16, 2026 Lanczos Iteration and Shift-Invert for Extreme Eigenvalues How a three-term recurrence reduces a large symmetric matrix to a tridiagonal one, which eigenvalues that reduction can resolve, and why shift-invert changes the question being asked. scientific computing
- Jul 6, 2026 Krylov Subspace Iteration and Why GMRES Restarts How a solver builds a subspace from repeated matrix-vector products, why the symmetric case needs three vectors of memory and the general case needs many, and when restarting destroys convergence. scientific computing
- Jan 25, 2023 Communication-Avoiding Algorithms and the Latency Floor How restructuring the arithmetic to block inner products and use fewer global synchronization steps changes the scaling exponent, and what it costs in numerical stability. scientific computing