{"paper":{"title":"A Multiscale Butterfly Algorithm for Multidimensional Fourier Integral Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Haizhao Yang, Lexing Ying, Yingzhou Li","submitted_at":"2014-11-26T23:02:52Z","abstract_excerpt":"This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form $(\\mathcal{L} f)(x) = \\int_{R^d}a(x,\\xi) e^{2\\pi \\i \\Phi(x,\\xi)}\\hat{f}(\\xi) d\\xi$, where $\\Phi(x,\\xi)$ is a phase function, $a(x,\\xi)$ is an amplitude function, and $f(x)$ is a given input. The frequency domain is hierarchically decomposed into a union of Cartesian coronas. The integral kernel $a(x,\\xi) e^{2\\pi \\i \\Phi(x,\\xi)}$ in each corona satisfies a special low-rank property that enables the application of a butterfly algorithm on the Cartesian phase-space grid. Thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7418","kind":"arxiv","version":2},"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"}