{"paper":{"title":"Fast QMC matrix-vector multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christoph Schwab, Frances Y. Kuo, Josef Dick, Quoc T. Le Gia","submitted_at":"2015-01-26T08:40:31Z","abstract_excerpt":"Quasi-Monte Carlo (QMC) rules $1/N \\sum_{n=0}^{N-1} f(\\boldsymbol{y}_n A)$ can be used to approximate integrals of the form $\\int_{[0,1]^s} f(\\boldsymbol{y} A) \\,\\mathrm{d} \\boldsymbol{y}$, where $A$ is a matrix and $\\boldsymbol{y}$ is row vector. This type of integral arises for example from the simulation of a normal distribution with a general covariance matrix, from the approximation of the expectation value of solutions of PDEs with random coefficients, or from applications from statistics. In this paper we design QMC quadrature points $\\boldsymbol{y}_0, ..., \\boldsymbol{y}_{N-1} \\in [0,1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06286","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}