In the next Chapters, we discuss the probably most important applications of approximate approximations, which lead to new classes of cubature formulas for integral operators of mathematical physics and for approximate solutions of initial boundary value problems for classical partial differential equations. By combining approximate approximations with separated representations, we derive a method for approximating volume potentials that is accurate and fast in high dimensions.

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Approximation of Integral Operators

  • Flavia Lanzara,
  • Vladimir Maz’ya,
  • Gunther Schmidt

摘要

In the next Chapters, we discuss the probably most important applications of approximate approximations, which lead to new classes of cubature formulas for integral operators of mathematical physics and for approximate solutions of initial boundary value problems for classical partial differential equations. By combining approximate approximations with separated representations, we derive a method for approximating volume potentials that is accurate and fast in high dimensions.