The theory and methods of minimizing a norm ∥f - φ∥ on the whole of a space of “simple” functions φ ∈ Φ depend crucially on the norm type. One should distinguish between the two cases:

• •Uniform approximation.\( \left\| f \right\| \equiv \mathop {\sup }\limits_x \left| {f(x)} \right| \) (there can be no scalar product inducing such a norm).

• •Least squares method. A norm in question is induced by some scalar product, for instance,\( \left\| f \right\| \equiv \left( {\int_a^b {|f(x)|^2 } dx} \right)^{\tfrac{1} {2}} \)

Unable to display preview. Download preview PDF.

Authors and Affiliations

1. Institute of Numerical Mathematics, Russian Academy of Sciences, Leninski Prospekt 32A, 117 334, Moscow, Russia

   Eugene E. Tyrtyshnikov

Reprints and permissions

© 1997 Springer Science+Business Media New York

Policies and ethics