Fast Computation of Volume Potentials by Approximate Approximations
This book introduces a new fast high-order method for approximating volume potentials and other integral operators with singular kernel. These operators arise naturally in many fields, including physics, chemistry, biology, and financial mathematics. A major impediment to solving real world problems...
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| Format: | Elektronički e-knjiga |
| Jezik: | engleski |
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Springer Nature Switzerland : Imprint: Springer,
2025.
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| Izdanje: | 1st ed. 2025. |
| Serija: | Lecture Notes in Mathematics,
2378 |
| Teme: | |
| Online pristup: | https://doi.org/10.1007/978-3-031-97442-7 |
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| 100 | 1 | |a Lanzara, Flavia. |e author. |0 (orcid)0000-0002-2052-4202 |1 https://orcid.org/0000-0002-2052-4202 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Fast Computation of Volume Potentials by Approximate Approximations |h [electronic resource] / |c by Flavia Lanzara, Vladimir Maz'ya, Gunther Schmidt. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (X, 264 p. 34 illus.). |b 8 illus. in color. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2378 | |
| 505 | 0 | |a Chapter 1. Introduction -- Chapter 2. Quasi-interpolation -- Chapter 3. Approximation of integral operators -- Chapter 4. Some other cubature problems -- Chapter 5. Approximate solution of non-stationary problems -- Chapter 6. Integral operators over hyper-rectangular domains. | |
| 520 | |a This book introduces a new fast high-order method for approximating volume potentials and other integral operators with singular kernel. These operators arise naturally in many fields, including physics, chemistry, biology, and financial mathematics. A major impediment to solving real world problems is the so-called curse of dimensionality, where the cubature of these operators requires a computational complexity that grows exponentially in the physical dimension. The development of separated representations has overcome this curse, enabling the treatment of higher-dimensional numerical problems. The method of approximate approximations discussed here provides high-order semi-analytic cubature formulas for many important integral operators of mathematical physics. By using products of Gaussians and special polynomials as basis functions, the action of the integral operators can be written as one-dimensional integrals with a separable integrand. The approximation of a separated representation of the density combined with a suitable quadrature of the one-dimensional integrals leads to a separated approximation of the integral operator. This method is also effective in high-dimensional cases. The book is intended for graduate students and researchers interested in applied approximation theory and numerical methods for solving problems of mathematical physics. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility. It includes screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, keyboard-friendly links and forms, and searchable, selectable text. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility Please Note that a more accessible version of this eBook is available as an EPUB. | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Approximation theory. | |
| 650 | 0 | |a Numerical analysis. | |
| 650 | 1 | 4 | |a Approximations and Expansions. |
| 650 | 2 | 4 | |a Numerical Analysis. |
| 700 | 1 | |a Maz'ya, Vladimir. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Schmidt, Gunther. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 830 | 0 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2378 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-97442-7 |
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