{"paper":{"title":"Fast Computation of Fourier Integral Operators","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Emmanuel Candes, Laurent Demanet, Lexing Ying","submitted_at":"2006-10-01T19:12:53Z","abstract_excerpt":"We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically a so-called Fourier integral operator (FIO) of the form $\\int e^{2\\pi i \\Phi(x,\\xi)} a(x,\\xi) \\hat{f}(\\xi) \\mathrm{d}\\xi$ at points given on a Cartesian grid. Here, $\\xi$ is a frequency variable, $\\hat f(\\xi)$ is the Fourier transform of the input $f$, $a(x,\\xi)$ is an amplitude and $\\Phi(x,\\xi)$ is a phase function, which is typically as large as $|\\xi|$; h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610051","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0610051/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}