Results 1  10
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39
A Note on Interpolating Scaling Functions
, 2000
"... In this paper, we are concerned with constructing interpolating scaling functions. The presented construction can be interpreted as a natural generalization of a wellknown univariate approach and applies to scaling matrices A satisfying det A = 2. The resulting scaling functions automatically sat ..."
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Cited by 33 (5 self)
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In this paper, we are concerned with constructing interpolating scaling functions. The presented construction can be interpreted as a natural generalization of a wellknown univariate approach and applies to scaling matrices A satisfying det A = 2. The resulting scaling functions automatically satisfy certain StrangFixconditions.
Coorbit Spaces and Banach Frames on Homogeneous Spaces with Applications to Analyzing Functions on Spheres
 ADV. COMP. MATH
, 2002
"... This paper is concerned with the construction of generalized Banach frames on homogeneous spaces. The major tool is a unitary group representation which is square integrable modulo a certain subgroup. By means of this representation, generalized coorbit spaces can be dened. Moreover, we can construc ..."
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Cited by 22 (7 self)
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This paper is concerned with the construction of generalized Banach frames on homogeneous spaces. The major tool is a unitary group representation which is square integrable modulo a certain subgroup. By means of this representation, generalized coorbit spaces can be dened. Moreover, we can construct a specic reproducing kernel which, after a judicious discretization, gives rise to Banach frames for these coorbit spaces. We also discuss nonlinear approximation schemes based on our new Banach frames. As a classical example, we apply our construction to the problem of analyzing and approximating functions on the spheres.
Symmetric Collocation Methods for Linear DifferentialAlgebraic Boundary Value Problems
, 2000
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Morozov’s Discrepancy Principle for Tikhonovtype functionals with nonlinear operators
, 2009
"... In this paper we deal with Morozov’s discrepancy principle as an aposteriori parameter choice rule for Tikhonov regularization with general convex penalty terms Ψ for nonlinear inverse problems. It is shown that a regularization parameter α fulfilling the discprepancy principle exists, whenever th ..."
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Cited by 16 (9 self)
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In this paper we deal with Morozov’s discrepancy principle as an aposteriori parameter choice rule for Tikhonov regularization with general convex penalty terms Ψ for nonlinear inverse problems. It is shown that a regularization parameter α fulfilling the discprepancy principle exists, whenever the operator F satisfies some basic conditions, and that for this parameter choice rule holds α → 0, δ q /α → 0 as the noise level δ goes to 0. It is illustrated that for suitable penalty terms this yields convergence of the regularized solutions to the true solution in the topology induced by Ψ. Finally, we establish convergence rates with respect to the generalized Bregman distance and a numerical example is presented.
Accurate attenuation correction in spect imaging using optimization of bilinear functions and assuming an unknown spatiallyvarying attenuation distribution
 In Nuclear Science Symposium, 1998. Conference Record. 1998 IEEE
, 1998
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A steepest descent algorithm for the global minimization of TikhonovPhillips functional
, 2000
"... We report on a new iterative approach for nding a global minimizer of the TikhonovPhillips functional with a special class of nonlinear operators F. Assuming that the operator itself can be decomposed into (or approximated by) a sum of a linear and a bilinear operator, we introduce a twostep itera ..."
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Cited by 9 (7 self)
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We report on a new iterative approach for nding a global minimizer of the TikhonovPhillips functional with a special class of nonlinear operators F. Assuming that the operator itself can be decomposed into (or approximated by) a sum of a linear and a bilinear operator, we introduce a twostep iteration scheme based on an outer iteration over the regularization parameter and an inner iteration with a steepest descent method. Finally we present numerical results for the reconstruction of the emission function in single photon emission computed tomography (SPECT).
Simulation of Industrial Crystal Growth by the Vertical Bridgman Method
, 2000
"... Single crystals of CadmiumZincTelluride are used as a substrate material for the production of infrared detectors and are usually grown by the vertical Bridgman method. We present a simulation of the whole growth process in two steps: In the first step, the (stationary) heat transport in the furn ..."
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Cited by 4 (4 self)
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Single crystals of CadmiumZincTelluride are used as a substrate material for the production of infrared detectors and are usually grown by the vertical Bridgman method. We present a simulation of the whole growth process in two steps: In the first step, the (stationary) heat transport in the furnace is modeled and calculated for different positions of the ampoule. This provides information about the most important parameter during this process: the temperature distribution in furnace and ampoule. The obtained temperatures are then used in the second step as boundary conditions for the (time dependent) simulation of temperature and convection in the ampoule. Only the use of adaptive finite element methods allows an efficient numerical simulation of the moving phase boundary, the convection in the melt and the temperature distribution in melt and crystal. Numerical results are presented for both furnace and ampoule simulations.
A multimesh finite element method for phasefield simulations
 In: Interface and Transport Dynamics, LNCSE
, 2003
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Uniqueness of local control sets
, 2002
"... The local controllability behavior near an equilibrium is discussed. If the Jacobian of the linearized system is hyperbolic, uniqueness of local control sets is established. 1 ..."
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Cited by 3 (3 self)
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The local controllability behavior near an equilibrium is discussed. If the Jacobian of the linearized system is hyperbolic, uniqueness of local control sets is established. 1