{"id":"W1973465423","doi":"10.1090/s0025-5718-07-02005-4","title":"On pseudospectra of matrix polynomials and their boundaries","year":2007,"lang":"en","type":"article","venue":"Mathematics of Computation","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":22,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada; Leverhulme Trust","keywords":"Mathematics; Eigenvalues and eigenvectors; Smoothness; Boundary (topology); Polynomial matrix; Matrix (chemical analysis); Polynomial; Boundary value problem; Matrix polynomial; Orthogonal polynomials; Pure mathematics; Mathematical analysis","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":[0.0007927449,0.00009187773,0.0002111492,0.0001225376,0.00006488667,0.00006863705,0.000202524,0.00003555938,0.000004318058],"category_scores_gemma":[0.00005818174,0.00007383696,0.00004090665,0.0001584487,0.0001159007,0.0001373482,0.00005758609,0.00004560929,0.000003173424],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000008747904,"about_ca_system_score_gemma":0.0000270241,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003318033,"about_ca_topic_score_gemma":7.579837e-7,"domain_scores_codex":[0.9992442,0.00002292108,0.000358462,0.0001147885,0.0001510147,0.0001085985],"domain_scores_gemma":[0.9988813,0.000578451,0.0002612716,0.000178014,0.00006884248,0.00003210688],"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":[0.00001082508,0.0001006037,0.000008100218,0.0001462142,0.0000151002,8.579478e-7,0.003666712,0.0002666103,0.002728057,0.9800684,0.00004193201,0.01294662],"study_design_scores_gemma":[0.0002696413,0.0001830868,0.0002455781,0.00006851895,0.000005239348,0.00001251975,0.0001720516,0.08375942,0.07644825,0.8387058,0.00003232491,0.00009751524],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3015098,0.00005403011,0.6972832,0.00006254769,0.00007557365,0.00008376258,0.00000209154,0.00002739887,0.0009015499],"genre_scores_gemma":[0.8368058,0.000002154371,0.1631326,0.00001301465,0.00001493915,5.916543e-7,7.864895e-7,0.000004552494,0.0000255522],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.535296,"threshold_uncertainty_score":0.3010984,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01012658525975362,"score_gpt":0.2662444689791648,"score_spread":0.2561178837194111,"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."}}