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Linear estimation and detection in Krylov subspaces with 11 tablesDietl, Guido Karl Erich January 2006 (has links)
Zugl.: München, Techn. Univ., Diss., 2006
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Linear estimation and detection in Krylov subspaces with 11 tablesDietl, Guido Karl Erich January 2006 (has links)
Zugl.: München, Techn. Univ., Diss., 2006 / Lizenzpflichtig
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Linear estimation and detection in Krylov subspaces : with ... 11 tables /Dietl, Guido K. E. January 2007 (has links)
Zugl.: München, Techn. Univ., Diss., 2006. / Literaturverz. S. [205] - 222.
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Krylov fabuliste : étude littéraire et historique /Colin, Maurice, January 1975 (has links)
Texte abrégé de: Thèse--Lettres--Paris IV, 1971. / Bibliogr. p. 644-654. Index.
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Linear estimation and detection in Krylov subspaces with 11 tables /Dietl, Guido Karl Erich. January 2007 (has links)
Techn. University, Diss., 2006--München. / Lizenzpflichtig.
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Analysis of the BiCG MethodRenardy, Marissa 31 May 2013 (has links)
The Biconjugate Gradient (BiCG) method is an iterative Krylov subspace method that utilizes a 3-term recurrence. BiCG is the basis of several very popular methods, such as BiCGStab. The short recurrence makes BiCG preferable to other Krylov methods because of decreased memory usage and CPU time. However, BiCG does not satisfy any optimality conditions and it has been shown that for up to n/2-1 iterations, a special choice of the left starting vector can cause BiCG to follow {em any} 3-term recurrence. Despite this apparent sensitivity, BiCG often converges well in practice. This paper seeks to explain why BiCG converges so well, and what conditions can cause BiCG to behave poorly. We use tools such as the singular value decomposition and eigenvalue decomposition to establish bounds on the residuals of BiCG and make links between BiCG and optimal Krylov methods. / Master of Science
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Model reduction of linear systems : an interpolation point of viewVandendorpe, Antoine 20 December 2004 (has links)
The modelling of physical processes gives rise to mathematical systems of increasing complexity. Good mathematical models have to reproduce the physical process as precisely as possible while the computing time and the storage resources needed to simulate the mathematical model are limited. As a consequence, there must be a tradeoff between accuracy and computational constraints. At the present time, one is often faced with systems that have an unacceptably high level of complexity. It is then desirable to approximate such systems by systems of lower complexity. This is the Model Reduction Problem. This thesis focuses on the study of new model reduction techniques for linear systems.
Our objective is twofold. First, there is a need for a better understanding of Krylov techniques. With such techniques, one can construct a reduced order transfer function that satisfies a set of interpolation conditions with respect to the original transfer function. A study of the generality of such techniques and their extension for MIMO systems via the concept of tangential interpolation constitutes the first part of this thesis. This also led us to study the generality of the projection technique for model reduction.
Most large scale systems have a particular structure. They can be modelled as a set of subsystems that interconnect to each other. It then makes sense to develop model reduction techniques that preserve the structure of the original system. Both interpolation-based and gramian-based structure preserving model reduction techniques are developed in a unified way. Second order systems that appear in many branches of engineering deserve a special attention. This constitutes the second part of this thesis.
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The function of the predicate in the fables of Krylov a text-grammatical study /Hamburger, Henri. January 1981 (has links)
Thesis (doctoral)--Rijksuniversiteit te Groningen, 1981. / Includes bibliographical references (p. 359-370).
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A Newton-Krylov Approach to Aerodynamic Shape Optimization in Three DimensionsLeung, Timothy 30 August 2010 (has links)
A Newton-Krylov algorithm is presented for aerodynamic shape optimization in three dimensions using the Euler equations. An inexact-Newton method is used in the flow solver, a discrete-adjoint method to compute the gradient, and the quasi-Newton optimizer to find the optimum. A Krylov subspace method with approximate-Schur preconditioning is used to solve both the flow equation and the adjoint equation. Basis spline surfaces are used to parameterize the geometry, and a fast algebraic algorithm is used for grid movement. Accurate discrete-adjoint gradients can be obtained in approximately one-fourth the time required for a converged flow solution. Single- and multi-point lift-constrained drag minimization optimization cases are presented for wing design at transonic speeds. In all cases, the optimizer is able to efficiently decrease the objective function and gradient for problems with hundreds of design variables.
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A Newton-Krylov Approach to Aerodynamic Shape Optimization in Three DimensionsLeung, Timothy 30 August 2010 (has links)
A Newton-Krylov algorithm is presented for aerodynamic shape optimization in three dimensions using the Euler equations. An inexact-Newton method is used in the flow solver, a discrete-adjoint method to compute the gradient, and the quasi-Newton optimizer to find the optimum. A Krylov subspace method with approximate-Schur preconditioning is used to solve both the flow equation and the adjoint equation. Basis spline surfaces are used to parameterize the geometry, and a fast algebraic algorithm is used for grid movement. Accurate discrete-adjoint gradients can be obtained in approximately one-fourth the time required for a converged flow solution. Single- and multi-point lift-constrained drag minimization optimization cases are presented for wing design at transonic speeds. In all cases, the optimizer is able to efficiently decrease the objective function and gradient for problems with hundreds of design variables.
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