return the remainder term from an interpolation structure

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Student[NumericalAnalysis][RemainderTerm] - return the remainder term from an interpolation structure

	Calling Sequence
	RemainderTerm(p, opts)

Parameters

p	-	a POLYINTERP structure
opts	-	(optional) equation(s) of the form keyword=value, where keyword is: errorboundvar; options for returning the remainder term

Description

•	The RemainderTerm command returns the remainder term from the POLYINTERP structure p.

•	The POLYINTERP structure is created using the PolynomialInterpolation command.

•	In order for the remainder term to exist, the POLYINTERP structure p must have an associated exact function, given through the PolynomialInterpolation command.

Options

•	errorboundvar = name

The name to assign to the independent variable in the remainder term.

Notes

•	POLYINTERP structures that were created with the CubicSpline command cannot be used with the RemainderTerm command, since they do not have a remainder term.

•	A remainder term is also called an error term.

Examples

(1)

$`&where`((1/5040)*(-2^(2-xi)*ln(2)^7*cos(Pi*xi)-7*2^(2-xi)*ln(2)^6*sin(Pi*xi)*Pi+21*2^(2-xi)*ln(2)^5*cos(Pi*xi)*Pi^2+35*2^(2-xi)*ln(2)^4*sin(Pi*xi)*Pi^3-35*2^(2-xi)*ln(2)^3*cos(Pi*xi)*Pi^4-21*2^(2-xi)*ln(2)^2*sin(Pi*xi)*Pi^5+7*2^(2-xi)*ln(2)*cos(Pi*xi)*Pi^6+2^(2-xi)*sin(Pi*xi)*Pi^7)*x*(x-.5)*(x-1.0)*(x-1.5)*(x-2.0)*(x-2.5)*(x-3.0), {0. <= xi and xi <= 3.0})$

(2)

(3)

$`&where`((1/720)*(.120*exp(.1*xi^2)+0.720e-1*xi^2*exp(.1*xi^2)+0.480e-2*xi^4*exp(.1*xi^2)+0.64e-4*xi^6*exp(.1*xi^2))*(x-1.)^2*(x-1.5)^2*(x-2.)^2, {1. <= xi and xi <= 2.})$

(4)

	See Also
	Student[NumericalAnalysis], Student[NumericalAnalysis][ApproximateExactUpperBound], Student[NumericalAnalysis][ApproximateValue], Student[NumericalAnalysis][ComputationOverview], Student[NumericalAnalysis][DataPoints], Student[NumericalAnalysis][ExactValue], Student[NumericalAnalysis][InterpolantRemainderTerm], Student[NumericalAnalysis][PolynomialInterpolation]