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Lec13 PDF

This document discusses numerical differentiation techniques including polynomial and Taylor series approximations to estimate derivatives, sources of error such as round-off errors, and Richardson extrapolation which uses more neighboring points than necessary but has advantages of simplicity and generality. It also covers deriving differentiation formulas using polynomial interpolation.

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Milind Jain
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71 views25 pages

Lec13 PDF

This document discusses numerical differentiation techniques including polynomial and Taylor series approximations to estimate derivatives, sources of error such as round-off errors, and Richardson extrapolation which uses more neighboring points than necessary but has advantages of simplicity and generality. It also covers deriving differentiation formulas using polynomial interpolation.

Uploaded by

Milind Jain
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Numerical Differentiation

Polynomial and Taylor Series


approximation
EXAMPLE:
Shall we reduce h further??

Round-Off error instability


Error estimate
In general ....
Advantages and disadvantages of Richardson extrapolation

Simplicity and generality are advantages

They use more neighboring points invovling a wider spacing


than perhaps necessary.
Deriving formulas using polynomial interploation

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