LEADER 00970nac# 22002411i 450 001 UON00095929 005 20231205102533.123 100 $a20020107f |0itac50 ba 102 $aIT 105 $a|||| ||||| 110 $ab|||||||||| 200 1 $aArcheologia. Università 463 1$1001UON00156388$12001 $aQuaderni di Cultura Mediolatina$eCollana della "Fondazione Ezio Franceschini"$fdiretta da Claudio Leonardi$v191 606 $aArcheologia$xCampi Flegrei$3UONC029126$2FI 620 $aIT$dRoma$3UONL000004 710 02$aAccademia Nazionale dei Lincei$cRoma$3UONV004441$04172 712 $a*Accademia *Nazionale dei *Lincei$3UONV246632$4650 791 02$aAccademia Pontificia dei Nuovi Lincei$zAccademia Nazionale dei Lincei $3UONV100849 791 02$aACCADEMIA DEI LINCEI$yAccademia Nazionale dei Lincei $3UONV042416 801 $aIT$bSOL$c20250328$gRICA 912 $aUON00095929 996 $aArcheologia. Università$91841945 997 $aUNIOR LEADER 03443nam 22005655 450 001 9911022457703321 005 20251208190012.0 010 $a3-031-97442-5 024 7 $a10.1007/978-3-031-97442-7 035 $a(CKB)40851708900041 035 $a(MiAaPQ)EBC32275519 035 $a(Au-PeEL)EBL32275519 035 $a(DE-He213)978-3-031-97442-7 035 $a(OCoLC)1545003009 035 $a(PPN)289059186 035 $a(EXLCZ)9940851708900041 100 $a20250831d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFast Computation of Volume Potentials by Approximate Approximations /$fby Flavia Lanzara, Vladimir Maz'ya, Gunther Schmidt 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (516 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2378 311 08$a3-031-97441-7 327 $aChapter 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. 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 $aNumerical Analysis 615 0$aApproximation theory. 615 0$aNumerical analysis. 615 14$aApproximations and Expansions. 615 24$aNumerical Analysis. 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