{"id":"W2013758652","doi":"10.1007/s10543-006-0106-8","title":"Solving differential-algebraic equations by Taylor series (II): Computing the System Jacobian","year":2006,"lang":"en","type":"article","venue":"BIT Numerical Mathematics","topic":"Modeling and Simulation Systems","field":"Computer Science","cited_by":43,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Jacobian matrix and determinant; Taylor series; Automatic differentiation; Nonlinear system; Mathematics; Algorithm; Applied mathematics; Algebraic equation; Code (set theory); Computation; Differential algebraic equation; Series (stratigraphy); Computer science; Differential equation; Ordinary differential equation; Mathematical analysis","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":[0.0004613023,0.0004877648,0.0005734496,0.0005163845,0.0004078413,0.0006960376,0.000720676,0.0004489941,0.00472103],"category_scores_gemma":[0.002593462,0.0002764002,0.0004475056,0.0005241443,0.0005598576,0.00111338,0.0006698004,0.0008654819,0.001118204],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000456369,"about_ca_system_score_gemma":0.0008432444,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002779746,"about_ca_topic_score_gemma":0.003223506,"domain_scores_codex":[0.9998272,0.00003104363,0.00001037108,0.00002540444,0.0000848428,0.00002112271],"domain_scores_gemma":[0.9995438,0.0002101263,0.0000306199,0.00007191175,0.0001172872,0.0000262091],"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":[0.0001730876,0.0001390991,0.002123832,0.0003422636,0.00005412492,0.0003149628,0.0003796428,0.4278834,0.03446222,0.1626023,0.007003935,0.3645212],"study_design_scores_gemma":[0.00001542849,0.00002447712,0.0001706649,0.00001001922,0.00001000094,0.0000607781,0.0000267123,0.9690165,0.007185025,0.02105862,0.002414848,0.000007001866],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02008891,0.00008279144,0.9728202,0.000118321,0.0001000747,0.00003003934,0.00002514116,0.0007568556,0.005977639],"genre_scores_gemma":[0.4052739,0.0002434982,0.5856936,0.0000827496,0.00009080642,0.00005442421,0.000131474,0.0006931685,0.007736354],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.00472103,"threshold_uncertainty_score":0.01579338,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01650819104786249,"score_gpt":0.227166666810932,"score_spread":0.2106584757630695,"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."}}