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Regularization in Banach spaces — convergence rates by approximative source conditions
Journal of Inverse and Ill-posed Problems, 2009The author considers the linear ill-posed equation \(Ax=y^\delta\), where \(A:X\rightarrow Y\) is a bounded linear operator between two reflexive Banach spaces, and the data \(y\) is unknown, with only the estimate \(\|y-y^\delta\|< \delta\) available.
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Mathematische Zeitschrift, 1968
In a preceding paper [8], we studied a new method of proving the existence of solutions of nonlinear functional equations involving a densely defined monotone operator T from a reflexive Banach space X to its conjugate space X*. This method, which uses approximating equations containing compact monotone operators in an auxiliary Hilbert space, we ...
Browder, F. E., Ton, B. A.
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In a preceding paper [8], we studied a new method of proving the existence of solutions of nonlinear functional equations involving a densely defined monotone operator T from a reflexive Banach space X to its conjugate space X*. This method, which uses approximating equations containing compact monotone operators in an auxiliary Hilbert space, we ...
Browder, F. E., Ton, B. A.
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Convergence rates for an iteratively regularized Newton–Landweber iteration in Banach space
Inverse Problems, 2013In this paper, we provide convergence and convergence rate results for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting. Numerical experiments illustrate the performance of the method.
Barbara Kaltenbacher, Ivan Tomba
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On Tikhonov regularization in Banach spaces – optimal convergence rates results
Applicable Analysis, 2009In the present article, we deal with convergence rates for a Tikhonov-like regularization approach for linear and non-linear ill-posed problems in Banach spaces. Under validity of a source condition, we derive convergence rates which are well known as optimal in a Hilbert space situation.
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Regularization of ill-posed problems in Banach spaces: convergence rates
Inverse Problems, 2005Given a (not necessarily reflexive) Banach space \(X\), a Hilbert space \(H\) and a linear bounded compact operator \(A: X\to H\), the author considers regularization methods for solving the equation \(Ax= y\); estimates between the regularized solutions and the true solutions of \(Ax= y\), using a priori information on the solutions (also called ...
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Tikhonov regularization in Banach spaces—improved convergence rates results
Inverse Problems, 2009In this paper, we deal with convergence rates for a Tikhonov-like regularization approach for linear ill-posed problems in Banach spaces. Here, we deal with the so-called distance functions which quantify the violation of an introduced reference source condition.
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American Journal of Mathematics, 1995
A convergence condition for adelic zeta functions associated to irreducible regular prehomogeneous vector spaces is given and applied to fundamental regular prehomogeneous vector spaces. Let \((G, X)\) be a regular irreducible prehomogeneous vector space defined on an algebraic number field \(k\) and let \(D\subset G\) be the derived subgroup of \(G\).
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A convergence condition for adelic zeta functions associated to irreducible regular prehomogeneous vector spaces is given and applied to fundamental regular prehomogeneous vector spaces. Let \((G, X)\) be a regular irreducible prehomogeneous vector space defined on an algebraic number field \(k\) and let \(D\subset G\) be the derived subgroup of \(G\).
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T-Regular-Closed Convergence Spaces
Proceedings of the American Mathematical Society, 1975Kent, Darrell C. +2 more
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Convex Tikhonov regularization in Banach spaces: New results on convergence rates
Journal of Inverse and Ill-posed Problems, 2015Abstract Tikhonov regularization in Banach spaces with convex penalty and convex fidelity term for linear ill-posed operator equations is studied. As a main result, convergence rates in terms of the Bregman distance of the regularized solution to the exact solution is proven by imposing a generalization of the established variational ...
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