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 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 9 (7 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.
A novel parallel QR algorithm for hybrid distributed memory HPC systems, Technical report 200915, Seminar for applied mathematics
, 2009
"... Abstract. A novel variant of the parallel QR algorithm for solving dense nonsymmetric eigenvalue problems on hybrid distributed high performance computing (HPC) systems is presented. For this purpose, we introduce the concept of multiwindow bulge chain chasing and parallelize aggressive early defla ..."
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Cited by 8 (3 self)
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Abstract. A novel variant of the parallel QR algorithm for solving dense nonsymmetric eigenvalue problems on hybrid distributed high performance computing (HPC) systems is presented. For this purpose, we introduce the concept of multiwindow bulge chain chasing and parallelize aggressive early deflation. The multiwindow approach ensures that most computations when chasing chains of bulges are performed in level 3 BLAS operations, while the aim of aggressive early deflation is to speed up the convergence of the QR algorithm. Mixed MPIOpenMP coding techniques are utilized for porting the codes to distributed memory platforms with multithreaded nodes, such as multicore processors. Numerous numerical experiments confirm the superior performance of our parallel QR algorithm in comparison with the existing ScaLAPACK code, leading to an implementation that is one to two orders of magnitude faster for sufficiently large problems, including a number of examples from applications.
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 8 (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).