[
    {
        "id": "osp-13436",
        "type": "article-journal",
        "title": "CG Versus MINRES: An Empirical Comparison",
        "author": [
            {
                "family": "Fong",
                "given": "David Chin-Lung"
            },
            {
                "family": "Saunders",
                "given": "Michael A."
            }
        ],
        "URL": "https://omanscience.com/en/articles/cg-versus-minres-an-empirical-comparison",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2012
                ]
            ]
        },
        "container-title": "Sultan Qaboos University Journal for Science",
        "volume": "16",
        "page": "44",
        "DOI": "10.24200/squjs.vol17iss1pp44-62",
        "publisher": "Sultan Qaboos University",
        "ISSN": "2308-3921",
        "abstract": "For iterative solution of symmetric systems the conjugate gradient method (CG) is commonly used when A is positive definite, while the minimum residual method (MINRES) is typically reserved for indefinite systems. We investigate the sequence of approximate solutions generated by each method and suggest that even if A is positive definite, MINRES may be preferable to CG if iterations are to be terminated early. In particular, we show for MINRES that the solution norms are monotonically increasing when A is positive definite (as was already known for CG), and the solution errors are monotonically decreasing. We also show that the backward errors for the MINRES iterates are monotonically decreasing."
    }
]