Optimization and Approximation by Pablo Pedregal

Author:Pablo Pedregal
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

5.6 Exercises

5.6.1 Exercises to Support the Main Concepts

1.Look at the variational problem consisting in minimizing the integral

among those functions u(x) such that , .

(a)It is very easy to check that the family for each is feasible for that problem. Find the value of t which is best.

(b)The family of functions

for each integer n is also feasible. Find the best n.

(c)For an arbitrary v(x), the function

is admissible. Can you find the best v(x)?

2.Consider the functional

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