One approach to doing this involves constructing a truncation of the tensor product of a one-dimensional multilevel basis. That approach was introduced by Smolyak and is known as "sparse grids." One class of methods for this involves subdividing an interval when two approximations of the output differ greatly; those methods are known as adaptive algorithms. When a function under consideration is (*) well-approximated by a polynomial, methods named for Gauss may be used. When many variables are involved, naïve methods for doing this fall victim to the "curse of dimensionality." Simple methods f
One approach to doing this involves constructing a truncation of the tensor product of a one-dimensional multilevel basis. That approach was introduced by Smolyak and is known as "sparse grids." One class of methods for this involves subdividing an interval when two approximations of the output differ greatly; those methods are known as adaptive algorithms. When a function under consideration is (*) well-approximated by a polynomial, methods named for Gauss may be used. When many variables are involved, naïve methods for doing this fall victim to the "curse of dimensionality." Simple methods for this include Simpson's rule and the trapezoidal rule. For 10 points, name this operation, in the one dimensional case of which the area under a curve is estimated.
One approach to doing this involves constructing a truncation of the tensor product of a one-dimensional multilevel basis.
numerical integration [or obvious equivalents; accept numerical quadrature; accept numerical discretization before “approximations”; prompt on “integration” alone]