- #1
bugatti79
- 794
- 1
Folks,
I am puzzled how the linear interpolation functions (see attached) were determined based on the following equation below
##\displaystyle \psi_i=\frac{(\xi-\xi_1)(\xi-\xi_2)...(\xi-\xi_{i-1})(\xi-\xi_{i+1})...(\xi-\xi_n)}{(\xi_i-\xi_1)(\xi_i-\xi_2)...(\xi_i-\xi_{i-1})(\xi_i-\xi_{i+1})...(\xi_i-\xi_n)}##
What do the dots represent above?
and
[itex]\psi_i(\xi_j)= 1[/itex] if ##i=j## and ##0## if ##i\ne j##
For example how is ##\psi_1(\xi)## determined?
thanks
I am puzzled how the linear interpolation functions (see attached) were determined based on the following equation below
##\displaystyle \psi_i=\frac{(\xi-\xi_1)(\xi-\xi_2)...(\xi-\xi_{i-1})(\xi-\xi_{i+1})...(\xi-\xi_n)}{(\xi_i-\xi_1)(\xi_i-\xi_2)...(\xi_i-\xi_{i-1})(\xi_i-\xi_{i+1})...(\xi_i-\xi_n)}##
What do the dots represent above?
and
[itex]\psi_i(\xi_j)= 1[/itex] if ##i=j## and ##0## if ##i\ne j##
For example how is ##\psi_1(\xi)## determined?
thanks