Basic Concepts Definition 1: AQR factorization(orQR decomposition) of a square matrixAconsists of an orthogonal matrixQand an upper triangular matrixRsuch thatA = QR. Property 1 (QR Factorization): For anyn × ninvertible matrixA, we can construct a QR factorization. Proof: LetA1, …, Anr...
decompositionwasintroducedtogetastandardeigenvalueproblem.Astep—by—stepprocedureofthismethodwas summarizedandprogrammedwithFORTRANlanguage.NumericalexamplesshowedthattheimprovedLanczos—QR algorithmispreciseandstable. Keywords:complexeigenvalueproblem;non—symmetricaldamping;Lanczosalgorithm;QRalgorithm ...
In [32], the problem of online singular value decomposition of time-varying matrices is formulated and solved. In [33,34], the QR decomposition is analyzed and discussed. A continuous model for solving complex-valued time-varying linear matrix equations via QR decomposition is proposed and ...
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