Curve Fitting Using Calculus in Normed Spaces

University essay from KTH/Optimeringslära och systemteori; KTH/Optimeringslära och systemteori; KTH/Optimeringslära och systemteori; KTH/Optimeringslära och systemteori

Abstract:

Curve fitting is used in a variety of fields, especially in physics, mathematics and economics.

The method is often used to smooth noisy data and for doing path planning. In this bachelor

thesis calculus of variations will be used to derive a formula for finding an optimal curve to fit a

set of data points. We evaluate a cost function (defined on the set of all curves

f on the interval

[

a; b]) given by F(f) =

R

b

a

(f00(x))2dx +

P

n

i

=1(f(xi)

  AT THIS PAGE YOU CAN DOWNLOAD THE WHOLE ESSAY. (follow the link to the next page)