Numerical Methods05 marksNumerical: Newton's backward differenceNewton's backward difference table construction
Construct Newton's backward difference table for the given data points and approximate the value of f(x) at x=45. | X | 10 | 20 | 30 | 40 | 50 | |-----|-------|-------|-------|-------|-------| | f(x) | 0.173 | 0.342 | 0.5 | 0.643 | 0.766 |
Construct Newton's backward difference table for the given data points and approximate the value of $f(x)$ at $x=45$.
| $X$ | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| $f(x)$ | 0.173 | 0.342 | 0.5 | 0.643 | 0.766 |
[5]
x 10 20 30 40 50 ----------------------- f(x) 0.173 0.342 0.500 0.643 0.766 $h = 10$, and we want $f(45)$. x f(x) $\nabla f$ $\nabla^2 f$ $\nabla^3 f$ $\nabla^4 f$ -------------------------------- 10 0.173 20 0.342 0.169 30 0.500 0.158 -0.011 40 0.643 0.143 -0.015 -0.004 50 0.766 0.123 -0.020 -0....