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Student[NumericalAnalysis][ApproximateExactUpperBound] - compute approximate, exact and upper bound remainder term values
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Calling Sequence
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ApproximateExactUpperBound(p)
ApproximateExactUpperBound(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) algebraic, list(algebraic); the point(s) at which the approximating polynomial, the exact value(s) of the function, and the upper bound(s) of the remainder term are computed
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Description
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The ApproximateExactUpperBound command computes three values: the approximating polynomial, the exact value of the function and the upper bound of the remainder term, for each point specified in pts.
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If pts is not specified, the extrapolated points in the given POLYINTERP structure are used instead.
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The computed values are returned in the form of a list: [pts, approximate values, exact values, upper bounds].
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Notes
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POLYINTERP structures whose interpolation method is the cubic spline method may not be used with this command.
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Examples
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![with(Student[NumericalAnalysis])](/support/helpjp/helpview.aspx?si=4315/file05062/math95.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=4315/file05062/math99.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=4315/file05062/math102.png)
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![[[.25, 2.685058594, 2.378414230, 1.793805001], [.75, -1.746582031, -1.681792830, .4892195457], [1.25, -1.166503906, -1.189207114, .2717886365]]](/support/helpjp/helpview.aspx?si=4315/file05062/math113.png)
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![ApproximateExactUpperBound(p1, [.5, 1.5])](/support/helpjp/helpview.aspx?si=4315/file05062/math117.png)
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![[[.5, 0., 0., 0.], [1.5, 0., 0., 0.]]](/support/helpjp/helpview.aspx?si=4315/file05062/math120.png)
| (3) |
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