{"id":"W4312105420","doi":"10.1016/j.cam.2022.114996","title":"Eigenvalue bounds for saddle-point systems with singular leading blocks","year":2022,"lang":"en","type":"article","venue":"Journal of Computational and Applied Mathematics","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Saddle point; Eigenvalues and eigenvectors; Saddle; Positive-definite matrix; Singular value; Matrix (chemical analysis); Block (permutation group theory); Singular point of a curve; Mathematical analysis; Applied mathematics; Combinatorics; Geometry; Mathematical optimization","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":[0.000899857,0.0001084585,0.0002612756,0.0001113369,0.0003601963,0.0001679661,0.000304057,0.00001757257,0.000008142571],"category_scores_gemma":[0.000009666837,0.00008387091,0.00005533455,0.0001345001,0.00003525337,0.0001191714,0.0000994359,0.0001447211,9.559021e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003751004,"about_ca_system_score_gemma":0.00009717605,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":1.760393e-7,"about_ca_topic_score_gemma":2.98421e-8,"domain_scores_codex":[0.9988839,0.00002103702,0.0004041974,0.0001173883,0.0004375977,0.0001358637],"domain_scores_gemma":[0.9988638,0.0003919535,0.0004537406,0.00009361158,0.0001265572,0.00007030202],"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":[0.00002290553,0.0001033999,0.00000155717,0.000103171,0.00005256815,0.000008552929,0.001010511,0.2267298,0.0001012799,0.769726,0.0002513989,0.001888794],"study_design_scores_gemma":[0.0009074609,0.0003670927,0.000005462102,0.00004797412,0.00003691125,0.001372101,0.000893905,0.4962138,0.0001610325,0.4966295,0.00319286,0.000171887],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0237699,0.0001697843,0.974851,0.0002040219,0.0001553086,0.0001896895,0.000004674128,0.00001820148,0.0006374586],"genre_scores_gemma":[0.49029,0.000001725376,0.509343,0.00008698097,0.0001169464,0.00001749259,0.000001874127,0.0000099185,0.0001320935],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.4665201,"threshold_uncertainty_score":0.3420157,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01457620939334481,"score_gpt":0.2336195757182267,"score_spread":0.2190433663248819,"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."}}