Tyler Chen's free monograph demystifies the Lanczos algorithm for matrix functions
tak3sh8 · x · 2026-10-13
Tyler Chen published a free arXiv monograph, The Lanczos algorithm for matrix functions: a handbook for scientists (arXiv:2410.11090, v1 Oct 2024, revised Aug 2026), aimed at scientists outside numerical analysis, grad students, and newcomers.
- Consolidates knowledge fragmented across largely disjoint communities that drove Lanczos-based methods, and corrects widespread incorrect beliefs about behavior in finite precision arithmetic
- Emphasizes conceptual understanding, especially finite precision behavior; a shared screenshot shows the proof that Lanczos-FA is exact for low-degree polynomials (Theorem 6.2)
- Openly available; publicly recommended by computational linear algebra researchers like Ethan Epperly
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