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Optimal recovery of linear functionals on sets of finite dimension. (English. Russian original) Zbl 1159.65018
Math. Notes 84, No. 4, 561-567 (2008); translation from Mat. Zametki 84, No. 4, 602-608 (2008).
Let $$X$$ be a linear space of dimension $$n+1$$ generated by $$f_0, f_1,\dots,f_n$$. Let $$L_1,\dots,L_n$$ be linear functionals linearly independent defined on $$X$$ and $$L_0\neq L_i$$, $$i=1,\dots,n$$, another linear functional on $$X$$. Let $$P=\{\sum^n_{i=0}a_if_i:a_i\in\mathbb R$$, $$|a_i|\leq |\beta_i|$$, $$i=0,\dots,n\}$$, where $$\beta n=1$$ and $$(\beta_0,\dots,\beta n_1)$$ is the solution of the system $$\sum^n_{i=0} \beta j$$ $$L_jf_i=0$$, $$j=1,\dots,n$$. The author presents an algorithm that recovers the functional $$L_0$$ on $$P$$ with the least error among all linear algorithms using the information $$(L_1f,\dots,L_nf)$$.
##### MSC:
 65D15 Algorithms for approximation of functions 65D05 Numerical interpolation 65Y20 Complexity and performance of numerical algorithms
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##### References:
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