Results 1  10
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27
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.
Efficient Numerical Algorithms for Balanced Stochastic Truncation
, 2001
"... We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses fullrank factors of the Gramians to be balanced versus each other and exploits the fact that for largescale systems these Gramians are often of low numerical rank ..."
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Cited by 30 (2 self)
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We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses fullrank factors of the Gramians to be balanced versus each other and exploits the fact that for largescale systems these Gramians are often of low numerical rank. We use the easytoparallelize sign function method as the major computational tool in determining these fullrank factors and demonstrate the numerical performance of the suggested implementation of balanced stochastic truncation model reduction.
Numerical Analysis of a Quadratic Matrix Equation
 IMA J. NUMER. ANAL
, 1999
"... The quadratic matrix equation AX² +BX +C = 0 in n x n matrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various nume ..."
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Cited by 22 (7 self)
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The quadratic matrix equation AX² +BX +C = 0 in n x n matrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various numerical solution techniques. In particular, we give a thorough treatment of functional iteration methods based on Bernoulli's method. Other methods considered include Newton's method with exact line searches, symbolic solution and continued fractions. We show that functional iteration applied to the quadratic matrix equation can provide an efficient way to solve the associated quadratic eigenvalue problem ( 2 A + B + C)x = 0.
Symmetric Collocation Methods for Linear DifferentialAlgebraic Boundary Value Problems
, 2000
"... ..."
Solving a Quadratic Matrix Equation by Newton’s Method with Exact Line Searches, Numerical Analysis Report 339
 Manchester Centre for Computational Mathematics
, 1999
"... with exact line searches ..."
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 12 (4 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.
Solving LinearQuadratic Optimal Control Problems on Parallel Computers
, 2007
"... We discuss a parallel library of efficient algorithms for the solution of linearquadratic optimal control problems involving largescale systems with statespace dimension up to O(10 4). We survey the numerical algorithms underlying the implementation of the chosen optimal control methods. The appr ..."
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Cited by 11 (10 self)
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We discuss a parallel library of efficient algorithms for the solution of linearquadratic optimal control problems involving largescale systems with statespace dimension up to O(10 4). We survey the numerical algorithms underlying the implementation of the chosen optimal control methods. The approaches considered here are based on invariant and deflating subspace techniques, and avoid the explicit solution of the associated algebraic Riccati equations in case of possible illconditioning. Still, our algorithms can also optionally compute the Riccati solution. The major computational task of finding spectral projectors onto the required invariant or deflating subspaces is implemented using iterative schemes for the sign and disk functions. Experimental results report the numerical accuracy and the parallel performance of our approach on a cluster of Intel Itanium2 processors.
Morozov's Discrepancy Principle for Tikhonov regularization of nonlinear operators
 NUMER. FUNCT. ANAL. AND OPTIMIZ
, 2001
"... We consider Morozov's discrepancy principle for Tikhonov{regularization of nonlinear operator equations. It is shown that minor restrictions to the operator F already guarantee the existence of a regularization parameter such that ky F (x )k c 1 holds. Moreover, some additional smoothness ..."
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Cited by 10 (7 self)
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We consider Morozov's discrepancy principle for Tikhonov{regularization of nonlinear operator equations. It is shown that minor restrictions to the operator F already guarantee the existence of a regularization parameter such that ky F (x )k c 1 holds. Moreover, some additional smoothness assumptions on the solution of F (x) = y ensure an optimal convergence rate. Finally we investigate some practically relevant examples, e.g. medical imaging (Single Photon Emission Computed Tomography). It is illustrated that the introduced conditions on F will be met in general by a large class of nonlinear operators.
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 (5 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).
Accurate attenuation correction in SPECT imaging using optimization of bilinear functions and assuming an unknown spatiallyvarying attenuation distribution
, 2000
"... We report on an iterative approach to reconstruct both the activity f(x) and the attenuation (x) directly from the emission sinogram data. The proposed algorithm is based on the iterative methods for solving linear operator equations. Whenever an operator F is the sum of a linear and a bilinear oper ..."
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Cited by 8 (4 self)
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We report on an iterative approach to reconstruct both the activity f(x) and the attenuation (x) directly from the emission sinogram data. The proposed algorithm is based on the iterative methods for solving linear operator equations. Whenever an operator F is the sum of a linear and a bilinear operator, a modified iteration sequence can be dened. Using a Taylor series about a fixed approximate distribution 0, the attenuated Radon transform can be well approximated as the sum of a linear operator in f and a bilinear operator in f and µ. The algorithm alternates between updates of f and updates of µ. In our test computations, the proposed algorithms achieve good reconstruction results both for generated and real data.