{"id":"W1987744915","doi":"10.1007/s002110100289","title":"Entrywise perturbation theory for diagonally dominant M-matrices with applications","year":2002,"lang":"en","type":"article","venue":"Numerische Mathematik","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":43,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Windsor","funders":"","keywords":"Diagonally dominant matrix; Mathematics; Diagonal; Inverse; Tridiagonal matrix; Combinatorics; Eigenvalues and eigenvectors; Electronic circuit; Pure mathematics; Geometry; Invertible matrix; Physics; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004512468,0.0001770361,0.000199117,0.00007967179,0.0002408281,0.0001604691,0.000694739,0.00005560902,0.0002034112],"category_scores_gemma":[0.00004901712,0.0001241008,0.00008577843,0.0003091859,0.00004993465,0.0004325323,0.00006994681,0.00008433303,0.0002081478],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001748322,"about_ca_system_score_gemma":0.00001690684,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.43399e-7,"about_ca_topic_score_gemma":1.889768e-7,"domain_scores_codex":[0.9988663,0.00005634808,0.0002433364,0.0003519234,0.0002266221,0.0002554959],"domain_scores_gemma":[0.9985619,0.0005048265,0.0001847265,0.0005712917,0.00009185176,0.00008536984],"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":[0.00001373284,0.0001896032,0.000004990456,0.00009371161,0.00002979859,0.000001995081,0.002144872,0.0000216714,0.0002654794,0.9511485,0.0008386988,0.04524699],"study_design_scores_gemma":[0.001399615,0.0002905284,0.00002429463,0.00009923949,0.00008552928,0.0001223057,0.0003486731,0.1289234,0.00809803,0.699714,0.1601451,0.0007492441],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0004651075,0.0006789723,0.9874488,0.0007744999,0.00005880741,0.0007318911,0.00001098003,0.0001637877,0.009667157],"genre_scores_gemma":[0.1761782,0.0001470021,0.7934942,0.000616818,0.0004395421,0.002793526,0.00001735134,0.00006625581,0.02624719],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.2514344,"threshold_uncertainty_score":0.5060685,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01238587040981794,"score_gpt":0.2248017604779382,"score_spread":0.2124158900681202,"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."}}