{"id":"W62443529","doi":"10.1007/978-1-4419-0158-3_29","title":"Generating Eigenvalue Bounds Using Optimization","year":2009,"lang":"en","type":"book-chapter","venue":"Springer optimization and its applications","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Eigenvalues and eigenvectors; Parametric statistics; Mathematics; Applied mathematics; Sensitivity (control systems); Matrix (chemical analysis); Shadow price; Mathematical optimization; Pure mathematics; Physics; Statistics; Engineering","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0028553,0.002259948,0.002223073,0.00294278,0.001034651,0.003388801,0.001932189,0.001856038,0.02243583],"category_scores_gemma":[0.01531992,0.001494417,0.001611278,0.002677982,0.00220418,0.005376777,0.00388344,0.004975978,0.008236452],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001083382,"about_ca_system_score_gemma":0.0005753702,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000541488,"about_ca_topic_score_gemma":0.0006506872,"domain_scores_codex":[0.9978829,0.0008648685,0.00008353795,0.0002933998,0.0007556917,0.0001196207],"domain_scores_gemma":[0.9932508,0.004730918,0.0002268639,0.001051677,0.0006081573,0.0001315734],"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":[0.00004565133,0.00005151774,0.0001104652,0.0001497529,0.00003397745,0.00003563802,0.0001451319,0.04867398,0.001854716,0.8372099,0.01759259,0.09409671],"study_design_scores_gemma":[0.000006481271,0.00001077486,0.00004614929,0.00004190931,0.000009354371,0.00001632927,0.00001276783,0.1313796,0.0009819827,0.8598513,0.007628328,0.00001515656],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.002457986,0.0006881648,0.9642103,0.0003618377,0.0003174817,0.00002825453,0.0001127378,0.000653395,0.03116995],"genre_scores_gemma":[0.2573563,0.004192611,0.6556396,0.0009863188,0.002114099,0.0007728821,0.001490104,0.005620618,0.07182738],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02243583,"threshold_uncertainty_score":0.07505536,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02370612038389466,"score_gpt":0.2485887075939056,"score_spread":0.2248825872100109,"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."}}