Sinopsis
^TFast and Approximate Computation of Laplace and Fourier Transforms ^Aby Ines Melzer ^DIn this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by numerical experiments.
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DEGREESTFast and Approximate Computation of Laplace and Fourier Transforms DEGREESAby Ines Melzer DEGREESDIn this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by nume
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Fast and approximate computation of Laplace and Fourier transforms
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Fast and Approximate Computation of Laplace and Fourier Transforms (Paperback)
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Logos Verlag Berlin GmbH, Berlin, 2016
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ISBN 13: 9783832542269
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Paperback. Condición: new. Paperback. In this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by numerical experiments. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 9783832542269
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Fast and Approximate Computation of Laplace and Fourier Transforms
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ISBN 10: 3832542264
ISBN 13: 9783832542269
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Fast and Approximate Computation of Laplace and Fourier Transforms (Paperback)
Publicado por
Logos Verlag Berlin GmbH, Berlin, 2016
ISBN 10: 3832542264
ISBN 13: 9783832542269
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Paperback. Condición: new. Paperback. In this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by numerical experiments. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Nº de ref. del artículo: 9783832542269
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