19/07/2019, 17:37
12/08/2019, 02:54
gugo82 ha scritto:Let $M$ be the space of monotone increasing functions of $[0,1]$ in itself and let $L$ be the space of linear functions over $[0,1]$.
1. For each $f in M$, find the projection of $f$ onto $L$, i.e. the function $f^** in L$ s.t. $int_0^1 (f(x) - f^**(x))^2 text(d) x = min_(phi in L) int_0^1 (f(x) - phi (x) )^2 text(d) x$.Testo nascosto, fai click qui per vederloHint: Let $phi (x) = a x + b$ and evaluate $a,b$ in such a way that $int_0^1 (f(x) - phi (x))^2 text(d) x$ attains its minimum value.
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