Multivariate rational approximation Academic Article uri icon

abstract

  • We estimate the error in approximating a function f f by rational functions of degree n n in the norm of L q ( ) , := [ 0 , 1 ] d {L_q}(Omega ),,Omega : = {[0,,1]^d} . Among other things, we prove that if f f is in the Sobolev space W p k ( ) W_p^k(Omega ) and if k / d 1 / p + 1 / q > 0 k/d - 1/p + 1/q > 0 , then f f can be approximated by rational functions of degree n n to an order O ( n k / d ) O({n^{ - k/d}}) .

published proceedings

  • Transactions of the American Mathematical Society

author list (cited authors)

  • DeVore, R. A., & Yu, X. M.

citation count

  • 5

complete list of authors

  • DeVore, Ronald A||Yu, Xiang Ming

publication date

  • January 1986