{"id":"W2018627399","doi":"10.1093/imanum/drt025","title":"GMRES convergence bounds that depend on the right-hand-side vector","year":2013,"lang":"en","type":"article","venue":"IMA Journal of Numerical Analysis","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Generalized minimal residual method; Mathematics; Eigenvalues and eigenvectors; Invertible matrix; Diagonalizable matrix; Applied mathematics; Residual; Convergence (economics); Rank (graph theory); Solver; Krylov subspace; Linear system; Combinatorics; Mathematical analysis; Mathematical optimization; Pure mathematics; Algorithm; Symmetric matrix","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.009547222,0.002855767,0.001168437,0.001513837,0.0006803672,0.00137759,0.001353846,0.001654118,0.003670493],"category_scores_gemma":[0.03673309,0.0004152192,0.0009179194,0.0007425093,0.00300076,0.002970442,0.002541178,0.003076891,0.001776462],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001200948,"about_ca_system_score_gemma":0.00107007,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002419763,"about_ca_topic_score_gemma":0.002175694,"domain_scores_codex":[0.9971301,0.00111506,0.0001467237,0.0002902327,0.001101432,0.0002165875],"domain_scores_gemma":[0.9796015,0.01344221,0.001233792,0.001584495,0.003852224,0.0002857075],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0005393807,0.00008920646,0.001862916,0.0008462569,0.0001184148,0.0003247608,0.0003296429,0.6737956,0.02248549,0.2096658,0.007130178,0.08281229],"study_design_scores_gemma":[0.000007476467,0.00005643003,0.0002138427,0.0001144631,0.00001503179,0.00007013253,0.00003507886,0.9640449,0.008178991,0.02390343,0.003330169,0.00003008144],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01219758,0.002259217,0.9716809,0.0009039975,0.0002909392,0.00005346979,0.0001192444,0.000767134,0.0117275],"genre_scores_gemma":[0.4310764,0.00332791,0.5503578,0.0008833095,0.0005117161,0.0004058387,0.0006564491,0.00226614,0.01051444],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009547222,"threshold_uncertainty_score":0.05049109,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01283529324500673,"score_gpt":0.2388455058763808,"score_spread":0.2260102126313741,"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."}}