{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007424088,0.0004378043,0.0004077434,0.0006001567,0.0003810953,0.0007508358,0.000715496,0.0004234318,0.002048403],"category_scores_gemma":[0.004031218,0.0002280248,0.0003503071,0.000556599,0.001023883,0.001619523,0.001021607,0.0008801235,0.000551086],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005508185,"about_ca_system_score_gemma":0.0005196616,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001313511,"about_ca_topic_score_gemma":0.001769047,"domain_scores_codex":[0.9995331,0.0001545939,0.00001636759,0.00005865559,0.0001844632,0.00005290567],"domain_scores_gemma":[0.9989932,0.0004133424,0.0001097213,0.0002175595,0.0001824776,0.00008380319],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000302207,0.0001128487,0.00161037,0.00008358941,0.00003179527,0.0002471606,0.0002786691,0.364595,0.03377146,0.4408459,0.001808551,0.1563125],"study_design_scores_gemma":[0.000009581941,0.00002798794,0.0001131904,0.000005199108,0.000001969779,0.00003848867,0.00002114217,0.9572448,0.003614109,0.03794515,0.0009691187,0.000009189289],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.08588912,0.00005546685,0.9119213,0.00006473207,0.000027239,0.00002206817,0.00002672507,0.0003278267,0.001665565],"genre_scores_gemma":[0.5403239,0.00007958743,0.4575222,0.00003378468,0.00002497739,0.00003956887,0.00007985102,0.0001029164,0.001793299],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.002048403,"threshold_uncertainty_score":0.006852567,"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."}}