Student[NumericalAnalysis][Bisection] - numerically approximate the real roots of an expression using the bisection method
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Calling Sequence
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Bisection(f, x=[a, b], opts)
Bisection(f, [a, b], opts)
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Parameters
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f
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algebraic; expression in the variable x representing a continuous function
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x
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name; the independent variable of f
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a
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numeric; one of two initial approximates to the root
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b
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numeric; the other of the two initial approximates to the root
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opts
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(optional) equation(s) of the form keyword=value, where keyword is one of functionoptions, lineoptions, maxiterations, output, pointoptions, showfunction, showlines, showpoints, stoppingcriterion, tickmarks, caption, tolerance, verticallineoptions, view; the options for approximating the roots of f
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Description
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The Bisection command numerically approximates the roots of an algebraic function, f, using a simple binary search algorithm.
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The Bisection command is a shortcut for calling the Roots command with the method=bisection option.
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Options
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A list of options for the plot of the expression f. By default, f is plotted as a solid red line.
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A list of options for the lines on the plot. By default the lines are dotted blue.
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The maximum number of iterations to to perform. The default value of maxiterations depends on which type of output is chosen:
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output = value: default maxiterations = 100
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output = sequence: default maxiterations = 10
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output = information: default maxiterations = 10
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output = plot: default maxiterations = 5
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output = animation: default maxiterations = 10
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output = value, sequence, plot, animation, or information
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The return value of the function. The default is value.
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output = value returns the final numerical approximation of the root.
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output = plot returns a plot of f with each iterative approximation shown and the relevant information about the numerical approximation displayed in the caption of the plot.
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output = animation returns an animation showing the iterations of the root approximation process.
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output = information returns detailed information about the iterative approximations of the root of f.
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The final plot options when output = plot or output = animation.
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A list of options for the points on the plot. By default, the points are plotted as green circles.
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showfunction = truefalse
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Whether to display f on the plot or not. By default, this option is set to true.
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Whether to display lines that accentuate each approximate iteration when output = plot. By default, this option is set to true.
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Whether to display the points at each approximate iteration on the plot when output = plot. By default, this option is set to true.
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stoppingcriterion = relative, absolute, or function_value
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The criterion that the approximations must meet before discontinuing the iterations. The following describes each criterion:
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relative : < tolerance
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absolute : < tolerance
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function_value : < tolerance
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By default, stoppingcriterion = relative.
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A caption for the plot. The default caption contains general information concerning the approximation. For more information about specifying a caption, see plot/typesetting.
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The error tolerance of the approximation. The default value is .
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verticallineoptions = list
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A list of options for the vertical lines on the plot. By default, the lines are dashed and blue.
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view = [realcons..realcons, realcons..realcons]
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The plot view of the plot when output = plot. See plot/options for more information.
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Examples
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>
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