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Newton_Gregory Polynomials

Posted by 41903013

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41903013

Newton_Gregory Polynomials
April 24, 2010 04:06PM

Registered: 15 years ago
Posts: 6
Rating: 0

I'm having trouble understanding how to derive an error term for a Newton-Gregory Forward Polynomial which is used in Trapezoid rule and Simpson's rule.

With regard to the Trapezoid rule: Why does the error term use the second derivative of the function rather than finctional differences (which are used in the Newton-Gregory Forward Polynomial). Where in the text book does it show how to derive this error term for a Newton-Gregory Forward Polynomial?

With regards to Simpson's rule: Why does the error term use the 4th derivative rather than the 3rd derivative as Simpson's rule only uses a 3 term Newton-Gregory Forward Polynomial where as the Trapezoid rule only uses 2 terms and the derivative in the errors differs by 2 degrees?