{"paper":{"title":"Multidimensional Phase Recovery and Interpolative Decomposition Butterfly Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Haizhao Yang, Juan Zhang, Kenneth L. Ho, Ze Chen","submitted_at":"2019-08-25T19:20:32Z","abstract_excerpt":"This paper focuses on the fast evaluation of the matvec $g=Kf$ for $K\\in \\mathbb{C}^{N\\times N}$, which is the discretization of a multidimensional oscillatory integral transform $g(x) = \\int K(x,\\xi) f(\\xi)d\\xi$ with a kernel function $K(x,\\xi)=e^{2\\pi\\i \\Phi(x,\\xi)}$, where $\\Phi(x,\\xi)$ is a piecewise smooth phase function with $x$ and $\\xi$ in $\\mathbb{R}^d$ for $d=2$ or $3$. A new framework is introduced to compute $Kf$ with $O(N\\log N)$ time and memory complexity in the case that only indirect access to the phase function $\\Phi$ is available. This framework consists of two main steps: 1)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09376","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.09376/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"}