{"id":"W1986211432","doi":"10.1007/s10092-004-0082-9","title":"On the growth factor in Gaussian elimination for matrices with sharp angular field of values","year":2004,"lang":"en","type":"article","venue":"CALCOLO","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Hermitian matrix; Mathematics; Positive-definite matrix; Combinatorics; Diagonal; Order (exchange); Theory of computation; Matrix (chemical analysis); Gaussian elimination; Gaussian; Complex matrix; Limit (mathematics); Normal matrix; Upper and lower bounds; Field (mathematics); Mathematical analysis; Pure mathematics; Physics; Eigenvalues and eigenvectors; Geometry; Chemistry; Quantum mechanics; Algorithm","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":[0.0001766313,0.00006145841,0.00008008521,0.00006343686,0.00004668794,0.00002826245,0.0003359398,0.00003446183,0.00001510296],"category_scores_gemma":[0.00008460265,0.00003610835,0.00002951283,0.0002092948,0.00002127929,0.0001241035,0.00002819593,0.00005411292,0.000003272559],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001907898,"about_ca_system_score_gemma":0.00002648331,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001226073,"about_ca_topic_score_gemma":0.000004561761,"domain_scores_codex":[0.9995246,0.00002747099,0.00009733732,0.0001338774,0.000107924,0.0001087925],"domain_scores_gemma":[0.9994274,0.0002961174,0.00005484959,0.0001662235,0.00003555965,0.00001979547],"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":[0.00002906258,0.0000597161,0.00007910343,0.00002959355,0.00000560397,0.000004358478,0.0008292753,0.0001165853,0.000229664,0.9954427,0.00008035382,0.00309399],"study_design_scores_gemma":[0.002146811,0.002789041,0.01177986,0.0002755848,0.00001548341,0.000009490398,0.0003406866,0.01306706,0.2789564,0.6898226,0.0003940145,0.0004028982],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.574778,0.00007066888,0.4182543,0.0047356,0.0001238873,0.000475341,0.000008063577,0.00004258947,0.001511519],"genre_scores_gemma":[0.993922,0.000003036006,0.005697703,0.0002641192,0.00002542374,0.00002584713,7.414022e-7,0.000003236691,0.00005787094],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.419144,"threshold_uncertainty_score":0.1472456,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01235893347209303,"score_gpt":0.2559370755966106,"score_spread":0.2435781421245176,"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."}}