Derivative of best approximation

  • Thread starter ekkilop
  • Start date
  • #1
29
0
Say that we have a continuous, differentiable function f(x) and we have found the best approximation (in the sense of the infinity norm) of f from some set of functions forming a finite dimensional vector space (say, polynomials of degree less than n or trigonometric polynomials of degree less than n or basically anything satisfying the Haar condition).

What can be said about how well the derivative, f'(x), is approximated by the derivative of the approximation?

Thank you.
 

Answers and Replies

  • #2
Svein
Science Advisor
Insights Author
2,188
725
What can be said about how well the derivative, f'(x), is approximated by the derivative of the approximation?
Not very much. Take g(x)=f(x)+sin(1000000x)/1000 as an approximation to f(x). Then g'(x) = f'(x)+1000*cos(x).
 

Related Threads on Derivative of best approximation

  • Last Post
Replies
9
Views
2K
Replies
2
Views
336
Replies
3
Views
7K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
2
Views
4K
P
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Top