Optimal order multilevel preconditioners for regularized ill-posed problems
نویسندگان
چکیده
منابع مشابه
Optimal order multilevel preconditioners for regularized ill-posed problems
In this article we design and analyze multilevel preconditioners for linear systems arising from regularized inverse problems. Using a scaleindependent distance function that measures spectral equivalence of operators, it is shown that these preconditioners approximate the inverse of the operator to optimal order with respect to the spatial discretization parameter h. As a consequence, the numb...
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Multilevel methods are popular for the solution of well-posed problems, such as certain boundary value problems for partial differential equations and Fredholm integral equations of the second kind. However, little is known about the behavior of multilevel methods when applied to the solution of linear ill-posed problems, such as Fredholm integral equations of the first kind, with a right-hand ...
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Many ill-posed problems are solved using a discretization that results in a least squares problem or a linear system involving a Toeplitz matrix. The exact solution to such problems is often hopelessly contaminated by noise, since the discretized problem is quite ill conditioned, and noise components in the approximate null-space dominate the solution vector. Therefore we seek an approximate so...
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Ill-conditioned matrices with block Toeplitz, Toeplitz block (BTTB) structure arise from the discretization of certain ill-posed problems in signal and image processing. We use a preconditioned conjugate gradient algorithm to compute a regularized solution to this linear system given noisy data. Our preconditioner is a Cauchy-like block diagonal approximation to an orthogonal transformation of ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2008
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-08-02100-5