Everything is Vecchia: Unifying low-rank and sparse inverse Cholesky approximations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914373162762240 |
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| author | Kaminetz, Eagan Webber, Robert J. |
| author_facet | Kaminetz, Eagan Webber, Robert J. |
| contents | The partial pivoted Cholesky approximation accurately represents matrices that are close to being low-rank. Meanwhile, the Vecchia approximation accurately represents matrices with inverse Cholesky factors that are close to being sparse. What happens if a partial Cholesky approximation is combined with a Vecchia approximation of the residual? This paper shows how the sum is exactly a Vecchia approximation of the original matrix with an augmented sparsity pattern. Thus, Vecchia approximations subsume a class of existing matrix approximations and have broad applicability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_05709 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Everything is Vecchia: Unifying low-rank and sparse inverse Cholesky approximations Kaminetz, Eagan Webber, Robert J. Numerical Analysis 65F55, 65C99, 15A23 The partial pivoted Cholesky approximation accurately represents matrices that are close to being low-rank. Meanwhile, the Vecchia approximation accurately represents matrices with inverse Cholesky factors that are close to being sparse. What happens if a partial Cholesky approximation is combined with a Vecchia approximation of the residual? This paper shows how the sum is exactly a Vecchia approximation of the original matrix with an augmented sparsity pattern. Thus, Vecchia approximations subsume a class of existing matrix approximations and have broad applicability. |
| title | Everything is Vecchia: Unifying low-rank and sparse inverse Cholesky approximations |
| topic | Numerical Analysis 65F55, 65C99, 15A23 |
| url | https://arxiv.org/abs/2603.05709 |