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Results tagged with approximation-theory
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user 38620
Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
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Find the maximum of $|a_{p}|$, if $a_0+a_1x+\dots+a_nx^n:[-1,1]\mapsto [-1,1]$
Let $n$ be a given positive integer, and let $f(x)=\displaystyle\sum_{k=0}^{n}a_{k}x^k$, where $a_{i}\in \mathbb{R}$, $0 \le i \le n$. If
$$|f(x)|\le 1,\qquad \text{for } ~|x|\le 1,$$
what is the max …
- 4,280