{"id":"W2007857521","doi":"10.1016/j.jat.2006.01.005","title":"On the Lebesgue constant for the Xu interpolation formula","year":2006,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":33,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Trigonometric interpolation; Interpolation (computer graphics); Polynomial interpolation; Lagrange polynomial; Birkhoff interpolation; Lebesgue integration; Chebyshev nodes; Constant (computer programming); Subspace topology; Linear interpolation; Polynomial; Applied mathematics; Mathematical analysis; Discrete mathematics; Pure mathematics; Combinatorics","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":[0.00338882,0.000105962,0.000188394,0.00007239581,0.0002301862,0.00007476345,0.0001954768,0.00005297795,0.0003450466],"category_scores_gemma":[0.001677144,0.00004677199,0.000202644,0.00008981824,0.00007556022,0.000119642,0.00001454823,0.0001644505,0.00001182585],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003823427,"about_ca_system_score_gemma":0.00003764894,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001186021,"about_ca_topic_score_gemma":0.000001971196,"domain_scores_codex":[0.9987956,0.0001498473,0.000636884,0.00006136414,0.0002348853,0.0001213693],"domain_scores_gemma":[0.9892201,0.00970748,0.0006274616,0.0002203528,0.0002012303,0.00002339014],"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":[0.0001554836,0.00009131744,0.0000017456,0.00003501998,0.00004290084,2.125055e-7,0.0002490648,0.00004162589,0.0004159481,0.9696513,0.02805619,0.001259206],"study_design_scores_gemma":[0.0003572738,0.0001139021,0.00001001165,0.00007763171,0.0000844938,0.00002640788,0.0005705605,0.007389327,0.001568082,0.9863133,0.003428889,0.00006007484],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0269493,0.00009015567,0.9538321,0.003212594,0.0003515184,0.0006599096,0.00001169654,0.00001742074,0.0148753],"genre_scores_gemma":[0.9844348,0.000006995022,0.01325338,0.0003925503,0.0005104287,0.00004546192,0.00000222673,0.00002377278,0.001330426],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9574854,"threshold_uncertainty_score":0.3778018,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03727938516899536,"score_gpt":0.2947455477832661,"score_spread":0.2574661626142707,"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."}}