LEADER 01176nam a2200313 i 4500 001 991000942079707536 005 20020507180256.0 008 960430s1979 us ||| | eng 020 $a0121588602 035 $ab10778925-39ule_inst 035 $aLE01304640$9ExL 040 $aDip.to Matematica$beng 082 0 $a514.2 084 $aAMS 54-06 084 $aAMS 54-XX 100 1 $aCantrell, James C.$0535551 245 10$aGeometric topology :$bproceedings of the 1977 Georgia Topology Conference held in Athens, Georgia, August 1-12, 1977 /$cedited by James C. Cantrell 260 $aNew York :$bAcademic Press,$c1979 300 $axiii, 698 p. :$bill. ;$c24 cm. 500 $aGeorgia Topology Conference, University of Georgia, 1977. 500 $aIncludes bibliographies 650 4$aManifolds$xCongresses 650 4$aTopology$xCongresses 907 $a.b10778925$b21-09-06$c28-06-02 912 $a991000942079707536 945 $aLE013 54-XX CAN11 (1979)$g1$i2013000047164$lle013$o-$pE0.00$q-$rl$s- $t0$u1$v0$w1$x0$y.i10878294$z28-06-02 996 $aGeometric topology$9921778 997 $aUNISALENTO 998 $ale013$b01-01-96$cm$da $e-$feng$gus $h0$i1 LEADER 03441nam 22005655 450 001 996673174803316 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 $a996673174803316 996 $aFast Computation of Volume Potentials by Approximate Approximations$94465018 997 $aUNISA