Best Basis Selection for Approximation in Lp Academic Article

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.

authors

• Devore, Ronald
• Petrova, Guergana

published proceedings

• Foundations of Computational Mathematics

author list (cited authors)

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

citation count

• 11

publication date

• January 2003

publisher

• Springer Nature  Publisher

published in

• Foundations of Computational Mathematics  Journal

Digital Object Identifier (DOI)

• 10.1007/s10208-002-0056-8

start page

• 161

end page

• 185

volume

• 3

issue

• 2

URL

• http://dx.doi.org/10.1007/s10208-002-0056-8