{"id":"W2013286893","doi":"10.1007/s00211-007-0112-z","title":"Bivariate Lagrange interpolation at the Padua points: the ideal theory approach","year":2007,"lang":"en","type":"article","venue":"Numerische Mathematik","topic":"Advanced Numerical Analysis Techniques","field":"Engineering","cited_by":59,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Lagrange polynomial; Interpolation (computer graphics); Trigonometric interpolation; Birkhoff interpolation; Bivariate analysis; Ideal (ethics); Polynomial interpolation; Applied mathematics; Spline interpolation; Nearest-neighbor interpolation; Linear interpolation; Inverse quadratic interpolation; Convergence (economics); Bilinear interpolation; Combinatorics; Algebra over a field; Mathematical analysis; Pure mathematics; Polynomial; Statistics; Law","routes":{"ca_aff":true,"ca_fund":false,"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":[0.001550309,0.0002508191,0.0002573183,0.00007103769,0.0002176343,0.00004963647,0.0004625162,0.00009755207,0.0002812481],"category_scores_gemma":[0.0001173375,0.0001313962,0.0001715489,0.0004555557,0.0001310106,0.0001588433,0.0001326211,0.0003506805,0.000217096],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000800682,"about_ca_system_score_gemma":0.000003858383,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001430938,"about_ca_topic_score_gemma":0.00001144056,"domain_scores_codex":[0.9985887,0.0001015006,0.0004296357,0.000218456,0.000303083,0.0003585574],"domain_scores_gemma":[0.9986484,0.0004830943,0.0001190176,0.0006490107,0.00003936132,0.0000611042],"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":[0.000507938,0.0007717046,0.00135573,0.0009306823,0.002580604,0.00003747807,0.03818373,0.005265332,0.1710701,0.4034229,0.07103594,0.3048378],"study_design_scores_gemma":[0.001147922,0.0001598524,0.003881031,0.0002131552,0.0006915577,0.0002425242,0.007871365,0.298088,0.06585,0.4363574,0.183179,0.002318161],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.008732024,0.000677988,0.9460403,0.0002860386,0.00007684349,0.0003374431,0.000005906618,0.0006902199,0.04315324],"genre_scores_gemma":[0.9480831,0.00006141884,0.05035609,0.0003398656,0.0001597474,0.0001018108,0.00001929284,0.00009110655,0.0007875871],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9393511,"threshold_uncertainty_score":0.5358182,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01052672511055293,"score_gpt":0.243051529999483,"score_spread":0.23252480488893,"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."}}