Taylor Series
The expression for the order of error given above is found by comparison of the procedure with a Taylor series.
- A Taylor series is a power series that can approximate a function, f(x), for values near to x=a.
- Its coefficients use the derivatives of at
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- The Taylor series says that if we know the values for all derivatives of at , we can approximate the function as closely as we desire.
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: The error term for a truncated Taylor series after the term
- where is a value between and . Since the value of is not known, there is still uncertainty in the exact value of the error.
2004-12-28