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On the matrix form of Kronecker lemma

100%
da Silva J., Oliveira A.
Discussiones Mathematicae Probability and Statistics
|
2009
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tom 29
|
nr 2
233-243
EN
A matrix generalization of Kronecker's lemma is presented with assumptions that make it possible not only the unboundedness of the condition number considered by Anderson and Moore (1976) but also other sequences of real matrices, not necessarily monotone increasing, symmetric and nonnegative definite. A useful matrix decomposition and a well-known equivalent result about convergent series are used in this generalization.
2
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Frequency analysis of preconditioned waveform relaxation iterations

88%
Augustynowicz A., Jackiewicz Z.
Applicationes Mathematicae
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1999
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tom 26
|
nr 2
229-242
EN
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting from semi-discretization of the heat equation in one and two dimensions. This theory and some heuristic arguments predict that preconditioning is most effective for the first few iterations.
3
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On Fourier coefficients of some classes of functions and their applications in approximation theory

75%
Ibrahimov E. J.
Commentationes Mathematicae
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2014
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tom 54
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nr 2
EN
In the paper, the behavior of Fourier coefficients of some classes of functions on an arbitrary orthogonal system is studied. The estimates of order of convergence to zero of Fourier-Gegenbauer coefficients are found. These estimates are precise and are of terminal character. The obtained results are used in convergence of Fourier-Gegenbauer series.
4
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Convergent Filter Bases

75%
Coghetto R.
Formalized Mathematics
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2015
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tom 23
|
nr 3
189-203
EN
We are inspired by the work of Henri Cartan [16], Bourbaki [10] (TG. I Filtres) and Claude Wagschal [34]. We define the base of filter, image filter, convergent filter bases, limit filter and the filter base of tails (fr: filtre des sections).
5
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Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem

75%
Jakubczyk B.
Annales Polonici Mathematici
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2000
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tom 74
|
nr 1
117-132
EN
We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.
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