Accuracy of preconditioned CG-type methods for least squares problems
نویسندگان
چکیده
منابع مشابه
Preconditioned Iterative Methods for Solving Linear Least Squares Problems
New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU fa...
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We consider the iterative solution of weighted Toeplitz least squares problems. Our approach is based on an augmented system formulation. We focus our attention on two types of preconditioners: a variant of constraint preconditioning, and the Hermitian/skew-Hermitian splitting (HSS) preconditioner. Bounds on the eigenvalues of the preconditioned matrices are given in terms of problem and algori...
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and Kk(BA,Br) = span{Br, (BA)Br, . . . , (BA)k−1Br}, (3) where B ∈ Rn×m is the mapping and preconditioning matrix, and apply Krylov subspace iteration methods on these subspaces. For overdetermined problems, applying the standard CG method to Kk(BA,Br) leads to the preconditioned CGLS [3] or CGNR [9] method while for underdetermined problems it leads to preconditioned CGNE [9] method. The GMRES...
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The standard iterative method for solving large sparse least squares problems min ∈Rn ‖ −A ‖2, A ∈ Rm×n is the CGLS method, or its stabilized version LSQR, which applies the (preconditioned) conjugate gradient method to the normal equation ATA = AT . In this paper, we will consider alternative methods using a matrix B ∈ Rn×m and applying the Generalized Minimal Residual (GMRES) method to min ∈R...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2003
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(03)80009-3