Lecture 15

Eugene E. Tyrtyshnikov
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Eugene E. Tyrtyshnikov: Russian Academy of Sciences, Institute of Numerical Mathematics

A chapter in A Brief Introduction to Numerical Analysis, 1997, pp 131-138 from Springer

Abstract: Abstract 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, $$ \left\| f \right\| \equiv \left( {\int_a^b {|f(x)|^2 } dx} \right)^{\tfrac{1} {2}} $$

Date: 1997
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DOI: 10.1007/978-0-8176-8136-4_15

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