Numerical Differentiation
Numerical Differentiation
Objective
 | Derivation of difference formulae using Taylor series expansion |
Vocabulary
Forward difference formula, backward difference formula, central differencing for first and second order derivatives, truncation error
Concepts
| Approximate derivative of function from derivative of interpolating polynomial |
| Derivation of difference formulae using Taylor series expansion |
| As spacing parameter decreases, truncation error decreases but rounding error increases. As spacing parameter increases, rounding error decreases but truncation error increases. |
| Optimal spacing parameter is no easily determined in general. |
| Numerical differentiation is a numerically unstable process, i.e., small change in function data can lead to large change in the corresponding derivative value. |