STI Publications - View Publication Form #16624
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Publication Information
| Title | Probing For Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement | ||||
| Abstract | Probing is a general technique that is used to reduce the variance of the Hutchinson stochastic estimator for the trace of the inverse of a large, sparse matrix A. The variance of the estimator is the sum of the squares of the off-diagonal elements of inv(A) . Therefore, this technique computes probing vectors that when used in the estimator they annihilate the largest off-diagonal elements. For matrices that display decay of the magnitude of |A^{-1}_{ ij}| with the graph distance between nodes i and j, this is achieved through graph coloring of increasing powers A^p. Equivalently, when a matrix stems from a lattice discretization, it is computationally beneficial to find a distance-p coloring of the lattice. In [23] a hierarchical coloring was proposed so that p can be increased at runtime as needed without discarding previous work. In this work, we study probing for the more general problem of computing the trace of a permutation of inv(A), say P*inv(A) . The motivation comes fro | ||||
| Author(s) | Heather Switzer, Andreas Stathopoulos, Eloy Romero, Jesse Laeuchli, Konstantinos Orginos | ||||
| Publication Date | August 2022 | ||||
| Document Type | Journal Article | ||||
| Primary Institution | Thomas Jefferson National Accelerator Facility, Newport News | ||||
| Affiliation | Comp Sci&Tech (CST) Div / Scientific Computing / Scientific Computing | ||||
| Funding Source | Other, SURA, Exascale Computing Project | ||||
| Proprietary? | No | ||||
| This publication conveys | Technical Science Results | ||||
| Document Numbers |
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| Associated with an experiment | No | ||||
| Associated with EIC | No | ||||
| Supported by Jefferson Lab LDRD Funding | No |
Journal Article
| Journal Name | SIAM Journal on Scientfic Computing |
| Refereed | No |
| Volume | 44 |
| Issue | 4 |
| Page(s) | B1096-B1121 |
Attachments/Datasets/DOI Link
| Document(s) |
DisplacementPaper-4.pdf
(STI Document)
2106.01275.pdf
(Accepted Manuscript)
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| DOI Link | |
| Dataset(s) | (none) |
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