{"id":"W2075038987","doi":"10.5539/jmr.v5n4p58","title":"Discussing a More Fundamental Concept Than the Minimal Residual Method to Solve Linear System in a Krylov Subspace","year":2013,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Taiwan University; National Science Council","keywords":"Mathematics; Linear subspace; Krylov subspace; Residual; Subspace topology; Projection (relational algebra); Combinatorics; Linear system; Applied mathematics; Discrete mathematics; Pure mathematics; Algorithm; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.008768795,0.000147512,0.0003602046,0.0004065025,0.000233177,0.0005430016,0.001764718,0.00006951145,0.00003583093],"category_scores_gemma":[0.0003814937,0.00008121673,0.0001187086,0.0007705012,0.0001304363,0.0004868562,0.0006165557,0.0008120866,0.00008462154],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001808824,"about_ca_system_score_gemma":0.0002064308,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004714954,"about_ca_topic_score_gemma":0.000007291396,"domain_scores_codex":[0.9964458,0.0006529555,0.0006756826,0.0002068826,0.001476956,0.0005417641],"domain_scores_gemma":[0.9969951,0.001595403,0.0002565358,0.0004953101,0.0004200951,0.000237536],"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":[0.0002564676,0.00270264,0.0008798955,0.001603591,0.0004833135,0.00147537,0.36267,0.002955478,0.02871921,0.5155956,0.01952666,0.06313173],"study_design_scores_gemma":[0.003085562,0.002254111,0.003090617,0.003208412,0.00004263516,0.003098707,0.2188997,0.6981576,0.02049228,0.04488308,0.001925856,0.0008614804],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.3307829,0.0001966489,0.6558035,0.0114029,0.0002053638,0.0007593792,0.000003947956,0.00002551114,0.000819864],"genre_scores_gemma":[0.3799755,0.000004140704,0.6190197,0.00005589789,0.0003327468,0.00002313097,1.959736e-7,0.00001937039,0.0005693645],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.6952021,"threshold_uncertainty_score":0.5236177,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07201811595646808,"score_gpt":0.4033788663043245,"score_spread":0.3313607503478564,"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."}}