{"id":"W2091356782","doi":"10.1090/s0025-5718-05-01748-5","title":"Algorithms for hyperbolic quadratic eigenvalue problems","year":2005,"lang":"en","type":"article","venue":"Mathematics of Computation","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":47,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary; University of Regina","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Positive-definite matrix; Eigenvalues and eigenvectors; Mathematics; Hermitian matrix; Quadratic equation; Lambda; Matrix (chemical analysis); Pure mathematics; Mathematical analysis; Applied mathematics; Combinatorics; Geometry; Quantum mechanics; 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":[0.0005610693,0.0001289197,0.0002365262,0.0001100179,0.00008345843,0.0000767728,0.0004290847,0.00004831364,0.000006603248],"category_scores_gemma":[0.00005701628,0.0001179648,0.00009178305,0.0002167006,0.00003276939,0.0003677329,0.00006371021,0.00005099655,0.00003525514],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000225242,"about_ca_system_score_gemma":0.00003942409,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001667826,"about_ca_topic_score_gemma":8.747042e-7,"domain_scores_codex":[0.9988902,0.00003437181,0.000453348,0.0001967986,0.0002400967,0.0001852282],"domain_scores_gemma":[0.9989641,0.0003078572,0.000251561,0.0002701526,0.0001550787,0.00005119859],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000003667524,0.0005562009,0.000004150697,0.0007017743,0.0000473484,6.278532e-7,0.006974253,0.06736103,0.001621763,0.6828353,0.0003852646,0.2395086],"study_design_scores_gemma":[0.0002764967,0.00008034603,0.000009687962,0.00004012856,0.000009591875,0.000008260365,0.00003438066,0.7576169,0.004058016,0.2373231,0.0004349951,0.0001081049],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01100398,0.00009461096,0.9870099,0.0003871502,0.00012698,0.0004940351,0.000003841608,0.000117191,0.0007623402],"genre_scores_gemma":[0.2774735,0.000003418077,0.7222024,0.00004584862,0.00008992627,0.00003574906,0.000005180352,0.0000111463,0.0001328404],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.6902559,"threshold_uncertainty_score":0.4810464,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03144884872393362,"score_gpt":0.2860411006219882,"score_spread":0.2545922518980546,"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."}}