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Description
| - One of the most important part of adaptive wavelet methods is an efficient approximate multiplication of stiffness matrices with vectors in wavelet coordinates. Although there are known algorithms to perform it in linear complexity, the application of them is relatively time consuming and its implementation is very difficult. Therefore, it is necessary to develop a wellconditioned wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, matrix-vector multiplication can be performed exactly with linear complexity. We present here a wavelet basis on the interval with respect to which both the mass and stiffness matrices corresponding to the one-dimensional Laplacian are sparse. Consequently, the stiffness matrix corresponding to the n-dimensional Laplacian in tensor product wavelet basis is also sparse. Moreover, the constructed basis has an excellent condition number. In this contribution, we shortly review this construction and show several numerical tests.
- One of the most important part of adaptive wavelet methods is an efficient approximate multiplication of stiffness matrices with vectors in wavelet coordinates. Although there are known algorithms to perform it in linear complexity, the application of them is relatively time consuming and its implementation is very difficult. Therefore, it is necessary to develop a wellconditioned wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, matrix-vector multiplication can be performed exactly with linear complexity. We present here a wavelet basis on the interval with respect to which both the mass and stiffness matrices corresponding to the one-dimensional Laplacian are sparse. Consequently, the stiffness matrix corresponding to the n-dimensional Laplacian in tensor product wavelet basis is also sparse. Moreover, the constructed basis has an excellent condition number. In this contribution, we shortly review this construction and show several numerical tests. (en)
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Title
| - ON A SPARSE REPRESENTATION OF LAPLACIAN
- ON A SPARSE REPRESENTATION OF LAPLACIAN (en)
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skos:prefLabel
| - ON A SPARSE REPRESENTATION OF LAPLACIAN
- ON A SPARSE REPRESENTATION OF LAPLACIAN (en)
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skos:notation
| - RIV/46747885:24510/12:#0000805!RIV13-MSM-24510___
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/46747885:24510/12:#0000805
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Wavelet; Hermite cubic splines; sparse representations. (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Finěk, Václav
- Černá, Dana
- Ondračková, Zdeňka
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issn
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http://localhost/t...ganizacniJednotka
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