{"id":"W4401934144","doi":"10.18280/mmep.110818","title":"Exploring Chaotic Dynamics in a Fourth-Order Newton Method for Polynomial Root Finding","year":2024,"lang":"en","type":"article","venue":"Mathematical Modelling and Engineering Problems","topic":"Advanced Numerical Analysis Techniques","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Root (linguistics); Dynamics (music); Chaotic; Order (exchange); Root-finding algorithm; Mathematics; Newton's method; Applied mathematics; Polynomial; Computer science; Mathematical analysis; Nonlinear system; Physics; Artificial intelligence; Economics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.000334571,0.0002663079,0.0003896898,0.0003056189,0.00003441162,0.0000972755,0.00009851668,0.00009532645,0.000003787447],"category_scores_gemma":[0.00004599549,0.000254532,0.00008989491,0.0004157083,0.00001214424,0.0002464297,0.0000329528,0.0003193583,0.00000429396],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001866671,"about_ca_system_score_gemma":0.000005800818,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001116001,"about_ca_topic_score_gemma":0.000005226365,"domain_scores_codex":[0.9987347,0.000007567699,0.0004093694,0.0003016629,0.0001171698,0.0004295491],"domain_scores_gemma":[0.9993697,0.0003537017,0.00001400953,0.0001478224,0.00001669437,0.0000980934],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00000219512,0.00001098483,0.000002553687,0.00173606,0.00003791478,0.000003715827,0.000388415,0.9843137,0.0005110856,0.007848993,0.000006593501,0.005137758],"study_design_scores_gemma":[0.0001023268,0.00002517685,8.441495e-7,0.0007753033,0.00003556202,0.00001127376,0.00002607725,0.9866225,0.0005202642,0.0112605,0.0003253258,0.000294824],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0183411,0.0005622174,0.9794187,0.0001093307,0.0001113165,0.000279524,0.000004486896,0.001077192,0.00009610546],"genre_scores_gemma":[0.4034913,0.0001462136,0.5957658,0.000002497698,0.00007376553,0.000351703,0.000006390323,0.0001090543,0.0000532312],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.3851502,"threshold_uncertainty_score":0.9999907,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05580092773407831,"score_gpt":0.2686920841056759,"score_spread":0.2128911563715976,"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."}}