Componentwise perturbation bounds for the $LU$, $LDU$ and $LDT^T$ decompositions
نویسندگان
چکیده
منابع مشابه
Componentwise perturbation analyses for the QR factorization
This paper gives componentwise perturbation analyses for Q and R in the QR factorization A = QR, QTQ = I , R upper triangular, for a given realm×nmatrixA of rank n. Such specific analyses are important for examplewhen the columns ofA are badly scaled. First order perturbation bounds are given for both Q and R. The analyses more accurately reflect the sensitivity of the problem than previous suc...
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Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reeect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller and more revealing bounds can be obtained. A survey is given of componentwise perturbation theory in n...
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Implicit methods for hyperbolic equations are analyzed using LU decompositions. It is shown that the inversion of the resulting tridiagonal matrices is usually stable even when diagonal dominance is lost. Furthermore, these decompositions can be used to construct stable algorithms in multidimensions. When marching to a steady state, the solution is independent of the time. Alternating direction...
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Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reflect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller and more revealing bounds can be obtained. A survey is given of componentwise perturbation theory in ...
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2000
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2000.24