{"paper":{"title":"Condition Estimates for Pseudo-Arclength Continuation","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"C. T. Kelley, I. C. F. Ipsen, I. G. Kevrekidis, K. I. Dickson","submitted_at":"2006-03-30T18:47:28Z","abstract_excerpt":"We bound the condition number of the Jacobian in pseudo arclength continuation problems, and we quantify the effect of this condition number on the linear system solution in a Newton GMRES solve.\n  In pseudo arclength continuation one repeatedly solves systems of nonlinear equations $F(u(s),\\lambda(s))=0$ for a real-valued function $u$ and a real parameter $\\lambda$, given different values of the arclength $s$. It is known that the Jacobian $F_x$ of $F$ with respect to $x=(u,\\lambda)$ is nonsingular, if the path contains only regular points and simple fold singularities. We introduce a new cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603716","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/0603716/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"}