{"doi":"10.1137/0907058","title":"GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems","abstract":"We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an $l_2 $-orthogonal basis of Krylov subspaces. It can be considered as a generalization of Paige and Saunders’ MINRES algorithm and is theoretically equivalent to the Generalized Conjugate Residual (GCR) method and to ORTHODIR. The new algorithm presents several advantages over GCR and ORTHODIR.","journal":"SIAM Journal on Scientific and Statistical Computing","year":1986,"id":11691,"datarank":1.395983884457509,"base_score":9.306559229716726,"endowment":9.306559229716726,"self_citation_contribution":1.395983884457509,"citation_network_contribution":0.0,"self_endowment_contribution":1.395983884457509,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":11009,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.0488,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"1986-07-01","fair_score":42.5,"fair_percentile":21.459982409850483,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":94278,"name":"Martin H. Schultz","orcid":null,"position":1,"is_corresponding":false},{"id":94279,"name":"Yousef Saad","orcid":"0000-0002-8614-5360","position":2,"is_corresponding":false},{"id":94277,"name":"Youcef Saad","orcid":null,"position":0,"is_corresponding":true}],"reference_count":12,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-03-01T18:20:47.508186Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":100.0,"fair_a":70.0,"fair_i":0.0,"fair_r":0.0,"fair_zscore":-0.2453,"fair_rationale":{"fair_score":42.5,"has_llm":false,"dimensions":{"F":{"name":"Findable","score":100.0,"criteria":[{"key":"f_has_doi","label":"Has a persistent DOI","kind":"deterministic","weight":1.0,"fraction":1.0,"signal":"DOI present","rationale":null},{"key":"f_repository_presence","label":"Indexed in repositories / literature DBs","kind":"deterministic","weight":1.0,"fraction":1.0,"signal":"datacite=0, pmcid=False, pmid=True","rationale":null},{"key":"f_persistent_ids","label":"Resolvable scholarly identifiers (OpenAlex)","kind":"deterministic","weight":0.5,"fraction":1.0,"signal":"OpenAlex id present","rationale":null}]},"A":{"name":"Accessible","score":70.0,"criteria":[{"key":"a_open_access","label":"Open Access / files deposited","kind":"deterministic","weight":1.5,"fraction":0.5,"signal":"files/OA location present but not flagged OA","rationale":null},{"key":"a_retrievable","label":"Free full text retrievable","kind":"deterministic","weight":1.0,"fraction":1.0,"signal":"3 OA location(s)","rationale":null}]},"I":{"name":"Interoperable","score":0.0,"criteria":[{"key":"i_linked_data","label":"Linked datasets / DataCite relations","kind":"deterministic","weight":1.0,"fraction":0.0,"signal":"linked_datasets=0, datacite=0","rationale":null},{"key":"i_standard_ids","label":"References data via standard accessions","kind":"deterministic","weight":1.0,"fraction":0.0,"signal":"accessions=0, trials=0","rationale":null}]},"R":{"name":"Reusable","score":0.0,"criteria":[{"key":"r_license","label":"Clear, open reuse license","kind":"deterministic","weight":1.5,"fraction":0.0,"signal":"no license","rationale":null},{"key":"r_downloads","label":"Demonstrated reuse (downloads)","kind":"deterministic","weight":0.5,"fraction":0.0,"signal":"downloads=0","rationale":null},{"key":"r_version","label":"Versioned / maintained","kind":"deterministic","weight":0.5,"fraction":0.0,"signal":"no version chain","rationale":null},{"key":"r_dataset","label":"Classified as a data resource","kind":"deterministic","weight":0.5,"fraction":0.0,"signal":"not a dataset","rationale":null}]}},"suggestions":["Attach a clear, open reuse license (e.g. CC-BY or CC0).","Link the underlying datasets via DOIs / DataCite relations.","Reference data using standard accessions (e.g. GEO, PDB, ClinicalTrials.gov).","Maintain explicit versioning for the dataset.","Make the paper/data Open Access or deposit the files in an open repository."],"model":null,"agent_version":"fair_agent_v1","fulltext_source":"abstract_only"},"fair_model":null,"fair_agent_version":"fair_agent_v1","fair_fulltext_source":"abstract_only","fair_has_llm":false,"fair_computed_at":"2026-06-10T23:26:47.130377Z","clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}