Name
Abstract | ||
|---|---|---|
This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic trace estimation in a second phase. In turn, Hutch++ only requires O (epsilon(-1)) matrix-vector products to approximate the trace within a relative error\varepsilon with high probability, provided that the matrix is symmetric positive semidefinite. This compares favorably with the O (epsilon(-2)) matrix-vector products needed when using stochastic trace estimation alone. In Hutch++, the number of matrix-vector products is fixed a priori and distributed in a prescribed fashion among the two phases. In this work, we derive an adaptive variant of Hutch++, which outputs an estimate of the trace that is within some prescribed error tolerance with a controllable failure probability, while splitting the matrix-vector products in a near-optimal way among the two phases. For the special case of a symmetric positive semidefinite matrix, we present another variant of Hutch++, called Nystrom++, which utilizes the so-called Nystrom approximation and requires only one pass over the matrix, as compared to two passes with Hutch++. We extend the analysis of Hutch++ to Nystrom++. Numerical experiments demonstrate the effectiveness of our two new algorithms. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1137/21M1447623 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | DocType | Volume |
trace estimation, adaptive algorithms, low-rank approximation | Journal | 43 |
Issue | ISSN | Citations |
3 | 0895-4798 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| David Persson | 1 | 0 | 0.34 |
| Alice Cortinovis | 2 | 0 | 0.68 |
| Daniel Kressner | 3 | 449 | 48.01 |