Fast Computation of Volume Potentials by Approximate Approximations / / by Flavia Lanzara, Vladimir Maz'ya, Gunther Schmidt

• Record Nr.: UNINA9911022457703321
• Autore: Lanzara Flavia
• Pubbl/distr/stampa: Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025
• ISBN: 3-031-97442-5
• Edizione: [1st ed. 2025.]
• Descrizione fisica: 1 online resource (516 pages)
• Collana: Lecture Notes in Mathematics, , 1617-9692 ; ; 2378
• Altri autori (Persone): Mazʹi︠a︡V. G; SchmidtGünther
• Disciplina: 511.4
• Soggetti: Approximation theory; Numerical analysis; Approximations and Expansions; Numerical Analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: 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.
• Sommario/riassunto: 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.