[PDF] Top 20 The idea behind Krylov methods
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The idea behind Krylov methods
... a Krylov space whose dimension is the degree of the minimal polynomial of A ...a Krylov method searches for the solution is small. In this case a Krylov method has the opportunity to converge ... See full document
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Restarting and error estimation in polynomial and extended Krylov subspace methods for the approximation of matrix functions
... an idea on how the error behaves, especially in later it- erations, this experiment also illustrates the danger of using the estimates as sole stopping criteria in the non-Hermitian case (or more generally in any ... See full document
206
Rational Krylov Methods for Operator Functions
... In this chapter we define operator functions f (A), where f is a complex-valued function and A is a linear operator on a complex Banach space B. The theory of operator functions includes matrix functions as a special ... See full document
185
Deflated block Krylov subspace methods for large scale eigenvalue problems
... block Krylov subspace may need a larger subspace than the deflated block Krylov subspace in order to produce comparable useful ...block Krylov subspace methods can be more efficient than the ... See full document
13
Short-term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices
... (Block methods for multiple right-hand sides can potentially give more rapid convergence than the aggregate cost of solving the systems one at a time [11, ... See full document
21
Regularization techniques based on Krylov subspace methods for ill-posed linear systems
... projection methods, recalling the basic principles underlying them. Krylov subspace methods are particularly important cases of pro- jection methods: indeed, the regularization methods ... See full document
156
Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
... rational Krylov methods reviewed here avoid this problem by using a projection or interpolation approach for computing approximations to the vector f (A)b from a low- dimensional search space without ... See full document
21
Block Krylov subspace methods for large-scale matrix computations in control
... direct methods for solving the Sylvester equation are ...standard methods are based on the Hessenberg–Schur decomposition to transform the original equation into a form that can be easily ...Iterative ... See full document
5
Block Krylov Subspace Spectral Methods for Variable-Coefficient Elliptic PDE
... Abstract —Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solv- ing time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for ... See full document
6
Aligning or Maligning - Getting Inside a New IDEA, Getting behind No Child Left behind and Getting outside of It All
... It calls for Individualized Education Programs (IEPs) 3 ° that are less specific and reviewed less frequently. It also eliminates some of the discipline protections f[r] ... See full document
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Krylov Iterative Methods for Support Vector Machines to Classify Galaxy Morphologies
... There are infinitely many possible hyperplanes that can be drawn in order to separate the two categories. It is desirable to find the optimal hyperplane, or the one that can provide the best possible classification. This ... See full document
15
Large-scale Topology Optimization using Preconditioned Krylov Subspace Methods with Recycling
... Ill-conditioning creates two problems for numerical simulation. First, ill-conditioning may seriously affect the accuracy of the computed solution. Second, the convergence of iterative methods is poor for ... See full document
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Krylov Subspace Solvers and Preconditioners
... An advantage of these methods is that they use short recurrences. A disadvantage is that there is only a semi- optimality property. As a result of this, more matrix vector products are needed and no convergence ... See full document
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Preprint E. Ullmann Krylov Subspace Recycling Methods in Stochastic Finite Element Computations ISSN
... We discretize problems (1.4) and (1.5) using the Stochastic Finite Element Method [14]. The remaining part of this paper is organized as follows. In Section 2 we review the basic SFEM dis- cretization steps and give the ... See full document
14
Determination of a good value of the time step and preconditioned Krylov subspace methods for the Navier-Stokes equations
... The purpose of this paper is the numerical study of the performance and practical aspects of certain iterative methods for solving systems of linear algebraic equa[r] ... See full document
13
Proper orthogonal decomposition versus Krylov subspace methods in reduced-order energy-converter models
... Arnoldi-based Krylov subspace methods are applied to the magnetodynamic finite element analysis of power electronic ...selection methods are investigated using either local or global quantities for ... See full document
6
Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning
... preconditioned Krylov subspace methods to the interior-point algorithm for linear programming ...The Krylov subspace methods do not suffer from rank-deficiency and therefore no preprocessing ... See full document
35
Order reduction of large scale second-order systems using Krylov subspace methods
... proposed methods are compared in Table 3 ...each Krylov subspace requires q ...two-sided methods introduced in Section 2 and also used in Section 5 , match q and 2q moments respectively, while not ... See full document
21
Comparison of Fixed Point Methods and Krylov Subspace Methods Solving Convection Diffusion Equations
... iterative methods are the stationary iterative me- thods (fixed point methods) [1]-[3], and the more general Krylov subspace methods ...iterative methods suffer from slow convergence ... See full document
14
The University Münster model surgery system for Orthognathic surgery. Part I – The idea behind
... The information for the necessary surgical displace- ment is generated in the cephalometric prediction schemes, using a special analysis protocol for lateral cephalometric radiographs. The two-dimensional cephalometric ... See full document
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