- Lothar Collatzedit
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Research Interests: Mathematics, Iteration, Linearization, DDC, Mathematik, and 4 moreEigenvalues and Eigenvectors, P, F, and Polynomial
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Research Interests: Applied Mathematics, Computer Science, Computing, Eigenvalues, Eigenvalue analysis, and 15 moreGraph Partitioning, Finite Element Model, End, Eigenvalues and Eigenvectors, Complex Structure, Frequency Response, Frequency Analysis, Domain Decomposition, Degree of Freedom, Acoustic Analysis, Frequency Response Analysis, a priori and a posteriori, Eigenvalue problem, Iterative Method, and Eigenvalue
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Research Interests: Mathematics, Applied Mathematics, Computer Science, Biology, Biological Chemistry, and 11 moreEigenvalues, Non, Numerical Analysis and Computational Mathematics, Regularization, Large Scale, Eigenvectors, Eigenvalues and Eigenvectors, Quadratic Optimization, Trust Region, Hessian matrix, and Eigenvalue problem
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A local convergence theorem for shooting methods proved in a foregoing paper of the authors is applied to nonlinear eigenvalue problems. Sufficient conditions for the isolatedness of a solution, the essential convergence condition, are... more
A local convergence theorem for shooting methods proved in a foregoing paper of the authors is applied to nonlinear eigenvalue problems. Sufficient conditions for the isolatedness of a solution, the essential convergence condition, are given for three classes of eigenvalueproblems. The efficiency of the method is demonstrated by several numerical examples.
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For large-scale eigenvalue problems the authors introduced in [16] a coarsegrained parallel algorithm for distributed memory computers based on substructuringand improved static condensation. It was observed that the loadbalancing may... more
For large-scale eigenvalue problems the authors introduced in [16] a coarsegrained parallel algorithm for distributed memory computers based on substructuringand improved static condensation. It was observed that the loadbalancing may become unsatisfactory if the master problem and the problemscorresponding to the substructures are of significantly different size. Inthis paper we improve the load balancing of the processors considerably byincorporating a
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A computational approach for solving regularized total least squares problems via a sequence of quadratic eigenvalue problems has recently been introduced by Sima, Van Huffel, and Golub. Combining this approach with the nonlinear Arnoldi... more
A computational approach for solving regularized total least squares problems via a sequence of quadratic eigenvalue problems has recently been introduced by Sima, Van Huffel, and Golub. Combining this approach with the nonlinear Arnoldi method and reusing information from all previous quadratic eigenvalue problems, together with an early update of search spaces we arrive at a very efficient method for large regularized total least squares problems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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ABSTRACT
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... (7) is the eigenvalue problem which results from the component mode synthesis method (CMS method for short) introduced by Craig and Bampton [5]. ... SIAM J. Sci. Comput., 25:2084 2106, 2004. [5] RR Craig Jr. and MCC Bampton. ...
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Incorporation of metal into brittle ceramics results in an increase in fracture toughness, which can lead to an increase in strength, reliability and thermal shock resistance of the composite compared to monolithic ceramics. The basic... more
Incorporation of metal into brittle ceramics results in an increase in fracture toughness, which can lead to an increase in strength, reliability and thermal shock resistance of the composite compared to monolithic ceramics. The basic material specific property, which controls the enhancement of the mechanical properties, is the bridging stress relation of the metal reinforcements. This relation was calculated from
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For solving the eigenvalue problem of a structural system having a large number of degrees of freedom the authors introduced in [6] the improved condensation method using the Rayleigh functional of the exactly condensed nonlinear... more
For solving the eigenvalue problem of a structural system having a large number of degrees of freedom the authors introduced in [6] the improved condensation method using the Rayleigh functional of the exactly condensed nonlinear eigenvalue problem. In this paper we discuss the implementation of the method for substructured problems on a distributed memory MIMD computer. Examples are presented which demonstrate the efficiency of the method at least if the number of substructures is not too large.
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Overview Quantum Dots are semiconductor heterostructures, in which the free carriers are confined to a small region by potential barriers in all three directions of space (3D). If the size of the region is less than the electron... more
Overview Quantum Dots are semiconductor heterostructures, in which the free carriers are confined to a small region by potential barriers in all three directions of space (3D). If the size of the region is less than the electron wavelength, the electronic states become quantized at discrete energy levels as it happens in an atom. Applications: micro and optoelectronic devices, modelling systems at the atomic level, proposed for qubit implementation in quantum computers How to model a quantum dot? Dots lie on wetting layer as a result of Stranski-Krastanov growth, a state of the art production technique using the relief of the elastic energy resulting from the large lattice mismatch between two materials. The deposited layer initially grows as a thin two dimensional (2D) wetting layer and after exceeding a critical thickness, the growth mode switches from 2D to 3D leading to the formation of a self-assembled quantum dot on the top of the wetting layer. Dots grow in large arrays rathe...
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In [1] G. Cybenko and C. Van Loan proposed a method to compute the minimal eigenvalue of a positive definite symmetric Toeplitz matrix which is a combination of a bisection method and Newton's method for the secular equation.... more
In [1] G. Cybenko and C. Van Loan proposed a method to compute the minimal eigenvalue of a positive definite symmetric Toeplitz matrix which is a combination of a bisection method and Newton's method for the secular equation. Interpreting the secular equation as exact condensation and replacing Newton's method by a root finding method based on a rational model of the secular equation the method of Cybenko and Van Loan is improved considerably. For test problems of dimensions up to 1024 the effort is reduced to approximately 35%.
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... Both phases of the method are accelerated considerably by rational Hermite interpolation of the secular equation. ... Column 3 and 4 contain the improvements gained with the enhanced upperbound (6) at the start of the method and,... more
... Both phases of the method are accelerated considerably by rational Hermite interpolation of the secular equation. ... Column 3 and 4 contain the improvements gained with the enhanced upperbound (6) at the start of the method and, additionally, the improved upper bound ...
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ABSTRACT