864 research outputs found
Implicit iteration methods in Hilbert scales under general smoothness conditions
For solving linear ill-posed problems regularization methods are required
when the right hand side is with some noise. In the present paper regularized
solutions are obtained by implicit iteration methods in Hilbert scales. % By
exploiting operator monotonicity of certain functions and interpolation
techniques in variable Hilbert scales, we study these methods under general
smoothness conditions. Order optimal error bounds are given in case the
regularization parameter is chosen either {\it a priori} or {\it a posteriori}
by the discrepancy principle. For realizing the discrepancy principle, some
fast algorithm is proposed which is based on Newton's method applied to some
properly transformed equations
Discrete alloy-type models: Regularity of distributions and recent results
We consider discrete random Schr\"odinger operators on with a potential of discrete alloy-type structure. That is, the
potential at lattice site is given by a linear combination
of independent identically distributed random variables, possibly with
sign-changing coefficients. In a first part we show that the discrete
alloy-type model is not uniformly -H\"older continuous, a frequently used
condition in the literature of Anderson-type models with general random
potentials. In a second part we review recent results on regularity properties
of spectral data and localization properties for the discrete alloy-type model.Comment: 20 pages, 0 figure
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