{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001287836,0.0004509361,0.001094634,0.0005598899,0.0004572972,0.0007651031,0.0008473667,0.0008076456,0.002640954],"category_scores_gemma":[0.008162091,0.000398293,0.0003231298,0.0008354568,0.001160754,0.000964634,0.001594036,0.0007582483,0.000290652],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006632576,"about_ca_system_score_gemma":0.0008529652,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0051742,"about_ca_topic_score_gemma":0.008309296,"domain_scores_codex":[0.9993181,0.00030407,0.00002689112,0.0000604981,0.0002206261,0.00006977255],"domain_scores_gemma":[0.997569,0.001569696,0.0001039198,0.0003092838,0.0003488911,0.000099075],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0005538812,0.00004846234,0.0006452126,0.0001115572,0.00001521072,0.00004505726,0.0001306564,0.8723898,0.004745369,0.06118858,0.001670674,0.05845563],"study_design_scores_gemma":[0.000008121116,0.00001196412,0.00006137572,0.000003204934,0.000001707535,0.000004835426,0.00001003326,0.9937434,0.0004168024,0.005451598,0.0002840473,0.000002977977],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06594218,0.0003016382,0.9295895,0.0001529404,0.00008507918,0.00002241406,0.00005234023,0.0001377151,0.003716214],"genre_scores_gemma":[0.6771378,0.0002404288,0.3172069,0.00004945175,0.00004960465,0.00006663262,0.0001133871,0.0001723375,0.00496335],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0051742,"threshold_uncertainty_score":0.01028812,"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."}}