{"id":"W4401337191","doi":"10.1007/s10208-024-09671-w","title":"Polynomial and Rational Measure Modifications of Orthogonal Polynomials via Infinite-Dimensional Banded Matrix Factorizations","year":2024,"lang":"en","type":"article","venue":"Foundations of Computational Mathematics","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Winnipeg; University of British Columbia","funders":"Division of Mathematical Sciences; Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada; Leverhulme Trust","keywords":"Mathematics; Orthogonal polynomials; Measure (data warehouse); Polynomial; Polynomial matrix; Matrix (chemical analysis); Matrix polynomial; Pure mathematics; Combinatorics; Algebra over a field; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004851767,0.0001892806,0.0002912617,0.0004706757,0.0002250726,0.0001591719,0.000365755,0.00008482255,0.0001231978],"category_scores_gemma":[0.0002012741,0.0001837127,0.000128384,0.0007126728,0.0002053504,0.0006359878,0.0001283394,0.0001289099,0.00003041783],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003537755,"about_ca_system_score_gemma":0.0005522037,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005286249,"about_ca_topic_score_gemma":0.000002121817,"domain_scores_codex":[0.9980258,0.00008374563,0.0008400237,0.0002987881,0.0005972503,0.0001544043],"domain_scores_gemma":[0.9971154,0.001689058,0.0002779494,0.0002924738,0.0005343847,0.00009068029],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000006945329,0.0002321325,0.00003652735,0.0002307813,0.000129781,0.000001101175,0.0008916339,0.0537846,0.002270318,0.9396914,0.0005401388,0.002184687],"study_design_scores_gemma":[0.000312066,0.00006327631,0.0006140198,0.0001183841,0.00005016527,0.00005135937,0.00003181293,0.7612658,0.0007837609,0.2359046,0.0005995215,0.0002052754],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01813975,0.0002594996,0.9792422,0.0008417608,0.0002958989,0.0002975323,0.0002073931,0.0001143871,0.0006015609],"genre_scores_gemma":[0.7333387,0.000005175925,0.2662266,0.00001716124,0.00007849224,0.00002059877,0.0001545678,0.00001361949,0.0001451014],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.7151989,"threshold_uncertainty_score":0.7491588,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02219312052247101,"score_gpt":0.2865821892287377,"score_spread":0.2643890687062667,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}