{"id":"W1976285441","doi":"10.12732/ijpam.v85i6.8","title":"ON THE CHEBYSHEV-HALLEY FAMILY OF ITERATION FUNCTIONS AND THE n-TH ROOT COMPUTATION PROBLEM","year":2013,"lang":"en","type":"article","venue":"International Journal of Pure and Apllied Mathematics","topic":"Iterative Methods for Nonlinear Equations","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Sherbrooke","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Chebyshev filter; Mathematics; Root (linguistics); Computation; Applied mathematics; Chebyshev iteration; Order (exchange); Newton's method; Root-finding algorithm; Chebyshev polynomials; Algebra over a field; Pure mathematics; Mathematical analysis; Algorithm; Nonlinear system; Finance; Physics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.00130271,0.0001327749,0.0002515748,0.0001261102,0.0001188712,0.0001600214,0.000205572,0.00004947853,0.00004660542],"category_scores_gemma":[0.0008577193,0.00006790095,0.0000938347,0.00009292896,0.000166818,0.0002049493,0.00004945883,0.0002335036,0.000006863413],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002492805,"about_ca_system_score_gemma":0.00003616943,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004238143,"about_ca_topic_score_gemma":0.000006547189,"domain_scores_codex":[0.9984589,0.0001823621,0.0006963122,0.00008635245,0.0004900534,0.00008601147],"domain_scores_gemma":[0.9955142,0.002739281,0.0007626505,0.0001153086,0.0008329283,0.00003562875],"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":[0.00006597598,0.0002859682,0.00004892747,0.00007094834,0.0003607973,0.000001972154,0.006981395,0.00026317,0.001698061,0.9818947,0.002924365,0.005403677],"study_design_scores_gemma":[0.001070442,0.0001150942,0.0002406828,0.0002054146,0.00009276547,0.00008290614,0.001694293,0.01612454,0.0004336334,0.9797351,0.0001237391,0.00008135115],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6384325,0.0001182177,0.3500248,0.007325388,0.0002443597,0.0005955468,0.00001576547,0.00001177003,0.003231646],"genre_scores_gemma":[0.8977085,0.00004081817,0.1013954,0.000197029,0.0002000747,0.00002561352,0.00000597503,0.00002012074,0.000406459],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.259276,"threshold_uncertainty_score":0.276892,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05357266741620402,"score_gpt":0.3336509679266782,"score_spread":0.2800783005104742,"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."}}