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A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods

Václav Červ, Karel Segeth (1982)

Aplikace matematiky

The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical experiments...

A survey on wavelet methods for (geo) applications.

Willi Freeden, Thorsten Maier, Steffen Zimmermann (2003)

Revista Matemática Complutense

Wavelets originated in 1980's for the analysis of (seismic) signals and have seen an explosion of applications. However, almost all the material is based on wavelets over Euclidean spaces. This paper deals with an approach to the theory and algorithmic aspects of wavelets in a general separable Hilbert space framework. As examples Legendre wavelets on the interval [-1,+1] and scalar and vector spherical wavelets on the unit sphere 'Omega' are discussed in more detail.

Neural networks using Bayesian training

Gabriela Andrejková, Miroslav Levický (2003)


Bayesian probability theory provides a framework for data modeling. In this framework it is possible to find models that are well-matched to the data, and to use these models to make nearly optimal predictions. In connection to neural networks and especially to neural network learning, the theory is interpreted as an inference of the most probable parameters for the model and the given training data. This article describes an application of Neural Networks using the Bayesian training to the problem...

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