Best Basis Selection for Approximation in Lp Academic Article uri icon

abstract

  • We study the approximation of a function class F in L p by choosing first a basis B and then using n -term approximation with the elements of B . Into the competition for best bases we enter all greedy (i.e., democratic and unconditional [20]) bases for L p . We show that if the function class F is well-oriented with respect to a particular basis B then, in a certain sense, this basis is the best choice for this type of approximation. Our results extend the recent results of Donoho [9] from L 2 to L p , p
    eq 2 . © Society for the Foundation of Computational Mathematics 2002.

author list (cited authors)

  • Ronald DeVore, .., Guergana Petrova, .., & Vladimir Temlyakov, ..

citation count

  • 8

publication date

  • May 2003