{"paper":{"title":"Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jussi Korpela, Lauri Oksanen, Matti Lassas","submitted_at":"2018-03-28T11:41:49Z","abstract_excerpt":"An inverse boundary value problem for the 1+1 dimensional wave equation $(\\partial_t^2 - c(x)^2 \\partial_x^2)u(x,t)=0,\\quad x\\in\\mathbb{R}_+$ is considered. We give a discrete regularization strategy to recover wave speed $c(x)$ when we are given the boundary value of the wave, $u(0,t)$, that is produced by a single pulse-like source. The regularization strategy gives an approximative wave speed $\\widetilde c$, satisfying a H\\\"older type estimate $\\| \\widetilde c-c\\|\\leq C \\epsilon^{\\gamma}$, where $\\epsilon$ is the noise level."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10541","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"}