{"id":"W2050429600","doi":"10.1007/s11786-007-0010-x","title":"Pseudospectra of Matrix Polynomials that Are Expressed in Alternative Bases","year":2007,"lang":"en","type":"article","venue":"Mathematics in Computer Science","topic":"Advanced Numerical Analysis Techniques","field":"Engineering","cited_by":15,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary; University of Toronto; Western University","funders":"","keywords":"Mathematics; Matrix polynomial; Polynomial matrix; Basis (linear algebra); Lagrange polynomial; Vandermonde matrix; Polynomial interpolation; Matrix (chemical analysis); Lebesgue integration; Interpolation (computer graphics); Matrix analysis; Scalar (mathematics); Polynomial; Pure mathematics; Algebra over a field; Mathematical analysis; Eigenvalues and eigenvectors; Linear interpolation; Geometry; Computer science","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":[0.001240091,0.001086813,0.0004765309,0.001875112,0.0007372926,0.002981349,0.0009689355,0.001174673,0.00820419],"category_scores_gemma":[0.005222395,0.0003982725,0.0006625323,0.00167996,0.001903115,0.004022053,0.001388872,0.002032682,0.001702421],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003714607,"about_ca_system_score_gemma":0.000551035,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001665024,"about_ca_topic_score_gemma":0.0002526083,"domain_scores_codex":[0.9985037,0.0003542471,0.00006836146,0.0001841143,0.0006698634,0.0002196944],"domain_scores_gemma":[0.997135,0.0008916549,0.0004201467,0.0006634067,0.0006023991,0.0002872415],"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":[0.00008955174,0.00003952796,0.0002744729,0.00004736476,0.00001833627,0.0002388333,0.0001873195,0.002736871,0.006324939,0.9736969,0.0009668157,0.01537893],"study_design_scores_gemma":[0.00001790343,0.00007887983,0.0005457074,0.00003659699,0.000019274,0.000828888,0.0001711597,0.04099243,0.005340067,0.9465528,0.005354095,0.00006219566],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.240518,0.0007093123,0.6965832,0.0008635216,0.001027092,0.00006993961,0.0003311349,0.0004561967,0.05944157],"genre_scores_gemma":[0.8682934,0.001252498,0.1043712,0.0005515206,0.0008742993,0.00009548949,0.0003525967,0.0004081422,0.0238008],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00820419,"threshold_uncertainty_score":0.02744573,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02013958722648946,"score_gpt":0.2952151792826439,"score_spread":0.2750755920561544,"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."}}