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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. 330 $aThis book introduces a new fast high-order method for approximating volume potentials and other integral operators with singular kernel. These operators arise naturally in many fields, including physics, chemistry, biology, and financial mathematics. A major impediment to solving real world problems is the so-called curse of dimensionality, where the cubature of these operators requires a computational complexity that grows exponentially in the physical dimension. The development of separated representations has overcome this curse, enabling the treatment of higher-dimensional numerical problems. The method of approximate approximations discussed here provides high-order semi-analytic cubature formulas for many important integral operators of mathematical physics. By using products of Gaussians and special polynomials as basis functions, the action of the integral operators can be written as one-dimensional integrals with a separable integrand. The approximation of a separated representation of the density combined with a suitable quadrature of the one-dimensional integrals leads to a separated approximation of the integral operator. This method is also effective in high-dimensional cases. The book is intended for graduate students and researchers interested in applied approximation theory and numerical methods for solving problems of mathematical physics. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2378 606 $aApproximation theory 606 $aNumerical analysis 606 $aApproximations and Expansions 606 $aNumerical Analysis 606 $aTeoria de l'aproximació$2thub 606 $aAnàlisi numèrica$2thub 606 $aAnàlisi volumètrica$2thub 606 $aOperadors integrals$2thub 608 $aLlibres electrònics$2thub 615 0$aApproximation theory. 615 0$aNumerical analysis. 615 14$aApproximations and Expansions. 615 24$aNumerical Analysis. 615 7$aTeoria de l'aproximació 615 7$aAnàlisi numèrica. 615 7$aAnàlisi volumètrica 615 7$aOperadors integrals 676 $a511.4 700 $aLanzara$b Flavia$0722520 701 $aMaz?i?a?$b V. G$041932 701 $aSchmidt$b Gu?nther$00 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911022457703321 996 $aFast Computation of Volume Potentials by Approximate Approximations$94465018 997 $aUNINA