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Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell's problem

Yanlai Chen, Jan S. Hesthaven, Yvon Maday, Jerónimo Rodríguez (2009)

ESAIM: Mathematical Modelling and Numerical Analysis


In a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup stability constants is essential. In [Huynh et al., C. R. Acad. Sci. Paris Ser. I Math.345 (2007) 473–478], the authors presented an efficient method, compatible with an off-line/on-line strategy, where the on-line computation is reduced to minimizing a linear functional under a few linear constraints. These constraints...

Improvement of Fisher's test of periodicity

Tomáš Cipra (1983)

Aplikace matematiky

Fisher's test of periodicity in time series and Siegel's version of this test for compound periodicities are investigated in the paper. An improvement increasing the power of the test is suggested and demonstrated by means of numerical simulations.

Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem

Hongjia Chen, Akira Imakura, Tetsuya Sakurai (2017)

Applications of Mathematics

One of the most efficient methods for solving the polynomial eigenvalue problem (PEP) is the Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR), which finds the eigenvalues contained in a certain domain using the contour integral. The SS-RR method converts the original PEP to a small projected PEP using the Rayleigh-Ritz projection. However, the SS-RR method suffers from backward instability when the norms of the coefficient matrices of the projected PEP vary widely. To improve the backward...

Improving feature selection process resistance to failures caused by curse-of-dimensionality effects

Petr Somol, Jiří Grim, Jana Novovičová, Pavel Pudil (2011)

Kybernetika

The purpose of feature selection in machine learning is at least two-fold - saving measurement acquisition costs and reducing the negative effects of the curse of dimensionality with the aim to improve the accuracy of the models and the classification rate of classifiers with respect to previously unknown data. Yet it has been shown recently that the process of feature selection itself can be negatively affected by the very same curse of dimensionality - feature selection methods may easily over-fit...

Improving the convergence of iterative methods

Jan Zítko (1983)

Aplikace matematiky

The author considers the operator equation x = T x + b . Methods for acceleration of convergence of the iterative process x n + 1 ) = T x n + b are investigated.

Including eigenvalues of the plane Orr-Sommerfeld problem

Peter P. Klein (1993)

Applications of Mathematics

In an earlier paper [5] a method for eigenvalue inclussion using a Gerschgorin type theory originating from Donnelly [2] was applied to the plane Orr-Sommerfeld problem in the case of a pure Poiseuile flow. In this paper the same method will be used to deal Poiseuile and Couette flow. Potter [6] has treated this case before with an approximative method.

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