{"id":"W2066021453","doi":"10.1016/j.amc.2007.07.040","title":"Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle","year":2007,"lang":"en","type":"article","venue":"Applied Mathematics and Computation","topic":"Control Systems and Identification","field":"Engineering","cited_by":361,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University","funders":"","keywords":"Sylvester matrix; Sylvester equation; Iterative method; Mathematics; Applied mathematics; Matrix (chemical analysis); Jacobi method; Sylvester's law of inertia; Least-squares function approximation; Matrix splitting; Algorithm; Mathematical analysis; Symmetric matrix; State-transition matrix; Eigenvalues and eigenvectors","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":[0.0004536296,0.00008043001,0.0001042377,0.00003984465,0.0002152684,0.00007365088,0.00008178141,0.00004021915,0.000002080525],"category_scores_gemma":[0.00001494975,0.00005463262,0.00003477727,0.0001648351,0.00004875236,0.00005793531,0.00002644241,0.00006895405,0.000002096061],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003290606,"about_ca_system_score_gemma":0.00000913153,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008506023,"about_ca_topic_score_gemma":0.00001173407,"domain_scores_codex":[0.9992309,0.00001434671,0.0004011771,0.00008950609,0.0001565506,0.0001075273],"domain_scores_gemma":[0.9994774,0.0001454652,0.0001403391,0.0001572798,0.00005831654,0.00002121976],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000004830726,0.00006895262,0.00001848927,0.0001589375,0.00006395831,5.783419e-8,0.003858573,0.04302173,0.5983064,0.3470761,0.0002529391,0.007168973],"study_design_scores_gemma":[0.0002360778,0.000003746067,0.0006948778,0.00002301507,0.000048399,0.000002743826,0.0002877575,0.9810843,0.0049315,0.01243133,0.0001701562,0.00008608173],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2911779,0.0001036352,0.7080297,0.00005469711,0.00008216822,0.000355733,0.000007202072,0.00002486106,0.0001640591],"genre_scores_gemma":[0.9951838,0.000004851933,0.004671488,0.000009098409,0.0000342393,0.00002536195,0.00001759451,0.00001202575,0.00004157105],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9380626,"threshold_uncertainty_score":0.2227854,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02355002850826686,"score_gpt":0.2752327507501776,"score_spread":0.2516827222419107,"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."}}