{"id":"W2022603337","doi":"10.3934/dcds.2015.35.4765","title":"Rigorous numerics for nonlinear operators with tridiagonal dominant linear part","year":2015,"lang":"en","type":"preprint","venue":"Discrete and Continuous Dynamical Systems","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"Agence Nationale de la Recherche","keywords":"Tridiagonal matrix; Mathematics; Linear operators; Operator (biology); Diagonal; Computation; Linear map; Nonlinear system; Inverse; Applied mathematics; Contraction (grammar); Algebra over a field; Pure mathematics; Mathematical analysis; Discrete mathematics; Algorithm; Physics; Geometry; Eigenvalues and eigenvectors; Quantum mechanics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001301267,0.0006414222,0.0004493497,0.0008016198,0.000544732,0.001042448,0.001115737,0.0009666572,0.002872303],"category_scores_gemma":[0.004156309,0.0003115364,0.0005569309,0.0003959615,0.001747263,0.002094632,0.001535338,0.001402731,0.0005542614],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008640235,"about_ca_system_score_gemma":0.001029686,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001123634,"about_ca_topic_score_gemma":0.001637512,"domain_scores_codex":[0.9994325,0.0001758623,0.00002898004,0.000033442,0.0002908618,0.00003834986],"domain_scores_gemma":[0.9989644,0.0004671523,0.0001291176,0.0001474127,0.0002259906,0.00006591884],"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":[0.00002704726,0.00005060275,0.000325564,0.0001362659,0.0000241228,0.00008487031,0.0001791247,0.1692192,0.007886227,0.8107424,0.001269748,0.01005467],"study_design_scores_gemma":[0.000007820045,0.00001113528,0.00006633346,0.00000861222,0.00000212898,0.00001668036,0.0000150532,0.8952565,0.0009445777,0.1023993,0.001264448,0.000007429368],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02351726,0.0002424641,0.9665568,0.0003513049,0.00007925845,0.00003303682,0.00005109182,0.0001985248,0.008970298],"genre_scores_gemma":[0.4506363,0.0005465722,0.5375807,0.0002040793,0.0001087322,0.0002533663,0.0001423358,0.0004088775,0.01011905],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002872303,"threshold_uncertainty_score":0.009608746,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0120367012027016,"score_gpt":0.2480885726719081,"score_spread":0.2360518714692065,"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."}}