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Student[NumericalAnalysis][UpperBoundOfRemainderTerm] - compute the upper bound of the remainder term at a given point
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Calling Sequence
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UpperBoundOfRemainderTerm(p)
UpperBoundOfRemainderTerm(p, pts)
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Parameters
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p
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a POLYINTERP structure
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pts
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(optional) numeric, list(numeric); a point or list of points at which the upper bound(s) of the remainder term are computed
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Description
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The UpperBoundOfRemainderTerm command returns the value(s) of upper bound of the remainder term of the approximated polynomial at the specified point(s) pts or at the extrapolated point(s) from the POLYINTERP structure, depending on whether pts is specified or not.
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The pts must be within the range of the approximating polynomial.
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If the POLYINTERP structure was created with the CubicSpline command, the boundary conditions must be clamped.
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Notes
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A remainder term is sometimes called an error term.
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Examples
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![with(Student[NumericalAnalysis])](/support/helpjp/helpview.aspx?si=5003/file05112/math131.png)
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![xy := [[0, 4.0], [.5, 0], [1.0, -2.0], [1.5, 0], [2.0, 1.0], [2.5, 0], [3.0, -.5]]](/support/helpjp/helpview.aspx?si=5003/file05112/math135.png)
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![xy := [[0, 4.0], [.5, 0], [1.0, -2.0], [1.5, 0], [2.0, 1.0], [2.5, 0], [3.0, -.5]]](/support/helpjp/helpview.aspx?si=5003/file05112/math138.png)
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![[[1.25, .2717886365]]](/support/helpjp/helpview.aspx?si=5003/file05112/math149.png)
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![[[1.7, .2519320805]]](/support/helpjp/helpview.aspx?si=5003/file05112/math156.png)
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