{"id":"W2165372370","doi":"10.1007/s00607-005-0140-4","title":"Optimal Quadratic and Cubic Spline Collocation on Nonuniform Partitions","year":2005,"lang":"en","type":"article","venue":"Computing","topic":"Advanced Numerical Analysis Techniques","field":"Engineering","cited_by":26,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; China Scholarship Council","keywords":"Mathematics; Collocation method; Collocation (remote sensing); Orthogonal collocation; Spline (mechanical); Applied mathematics; Boundary value problem; Quadratic equation; Uniqueness; Mathematical analysis; Nonlinear system; Ordinary differential equation; Geometry; Differential equation; Computer science","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":[0.00004441864,0.00007751949,0.0001001751,0.00005360331,0.00007554327,0.00001799638,0.00004433977,0.00002483342,0.00001180537],"category_scores_gemma":[0.00001697902,0.00007770446,0.00002106866,0.0001595215,0.00001819608,0.0000719185,0.00001929966,0.00008772763,0.00002962491],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005120324,"about_ca_system_score_gemma":0.000002557755,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001384975,"about_ca_topic_score_gemma":0.00000401424,"domain_scores_codex":[0.999569,0.000005966541,0.0001461407,0.00009725114,0.00005957652,0.0001220635],"domain_scores_gemma":[0.9997742,0.00004916558,0.00002094412,0.00009726451,0.00001775068,0.0000406347],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000001293971,0.00002029701,0.00008110669,0.00001182543,0.00001137335,7.386747e-7,0.0001078015,0.9325872,0.002170302,0.0006912913,0.0002286289,0.06408812],"study_design_scores_gemma":[0.00007006426,0.00002530393,0.0005302833,0.0000292751,0.000009421256,0.000002459855,0.00002920702,0.9910203,0.006597022,0.0001495955,0.001437742,0.00009938325],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4761236,0.00009514396,0.5210119,0.0001402685,0.0000207412,0.00006962967,8.010017e-7,0.0004748674,0.002063025],"genre_scores_gemma":[0.9176408,0.00001487277,0.08214319,0.00005170267,0.00009987863,0.000004044368,0.000006178939,0.00001166203,0.00002765904],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.4415172,"threshold_uncertainty_score":0.3168696,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007540692905724686,"score_gpt":0.2451677816059539,"score_spread":0.2376270887002292,"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."}}