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Add block Lanczos quadrature - #193

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split-138/lanczos-qfafrom
split-138/lanczos-block-qfa
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split-138/lanczos-qfafrom
split-138/lanczos-block-qfa

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@rileyjmurray rileyjmurray commented Oct 1, 2026 •

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BlockLanczosQFA approximates B^T f(A) B using the block Lanczos recurrence, avoiding reconstruction of the large matrix f(A)B. It supports fixed depth, a heuristic window stop, and a Gauss–Radau bracket check with explicit certification status. The bracket interpretation depends on the function and spectral assumptions; the heuristic stop supplies no certificate.

This extracts the block quadrature component from #138. It is based on #192 and reuses the block recurrence introduced in #191. The optional banded eigensolver is in #195.

Validation. All 537 core Release tests passed locally with Spack Clang 19.1.3 on macOS. Tests compare with independent dense matrix functions and scalar quadrature, and exercise depth caps, failed positive-definiteness checks, stopping controls, and workspace reuse.

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