interpolation: accuracy of deg-20 interpolating polynomial

C

calchere

Junior Member
Joined
Sep 13, 2006
Messages
50
An interpolating polynomial of degree 20 is to be used to approximate e^(-x) on the interval [0, 2]. How accurate will it be.

\(\displaystyle [f(x) - p(x)| \le \frac{1}{{4(n + 1)}}M(\frac{{b - a}}{n})^{n + 1}\)

|I don't know how to find M in this equation, but i'm not even sure I can use this equation.
The answer is 4.3*10^(-14)

Any help would be appreciated.
Thanks
 
calchere said:
An interpolating polynomial of degree 20 is to be used to approximate e^(-x) on the interval [0, 2]. How accurate will it be.

\(\displaystyle [f(x) - p(x)| \le \frac{1}{{4(n + 1)}}M(\frac{{b - a}}{n})^{n + 1}\)

|I don't know how to find M in this equation, but i'm not even sure I can use this equation.
The answer is 4.3*10^(-14)

Any help would be appreciated.
Thanks
Click to expand...
Use Taylor's expansion and the error will be bounded by the maximum value of the residual term.
 
You must log in or register to reply here.
Top