{"paper":{"title":"A Numerical Model for the Construction of Finite Blaschke Products with Preassigned Distinct Critical Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"Christer Glader, Ray P\\\"orn","submitted_at":"2018-03-16T13:24:11Z","abstract_excerpt":"We present a numerical model for determining a finite Blaschke product of degree $n+1$ having $n$ preassigned distinct critical points $z_1,\\dots,z_n$ in the complex (open) unit disk $\\mathbb{D}$. The Blaschke product is uniquely determined up to postcomposition with conformal automorphisms of $\\mathbb{D}$. The proposed method is based on the construction of a sparse nonlinear system where the data dependency is isolated to two vectors and on a certain transformation of the critical points. The efficiency and accuracy of the method is illustrated in several examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06211","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"}