Using interpolating functions in Mathematica

Mathematica
Thread starter fuzzyfunnel
Start date Feb 5, 2010
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Functions Mathematica

In summary, an interpolating function in Mathematica is a function that approximates a set of data points by passing through each point, allowing for values between the given data points or a smooth curve representation. To create one, the "Interpolation" command can be used with the option to specify the order. The accuracy can be adjusted with the "AccuracyGoal" and "PrecisionGoal" options. To plot an interpolating function, the "Plot" command can be used with options for customization. Multiple interpolating functions can also be combined using the "Piecewise" command with the option to adjust the smoothness.

Feb 5, 2010

fuzzyfunnel

I have an interpolating function in mathematica and just want to find when it takes a certain value, seems simple, but I can't do it.

i.e. I solved an equation numerically for z(rho) and got interpolating function x for z.

Now I want to know for which value of rho, z(rho)=1 for example.

Anyone know how?

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Feb 5, 2010

Dale

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Use FindRoot

1. What is an interpolating function in Mathematica?

An interpolating function in Mathematica is a function that approximates a set of data points by passing through each point. It can be used to find values between the given data points or to create a smooth curve that represents the data.

2. How do I create an interpolating function in Mathematica?

To create an interpolating function in Mathematica, you can use the command "Interpolation[data]" where "data" is the set of data points you want to approximate. You can also specify the order of the interpolation by using "Interpolation[data, order]".

3. Can I adjust the accuracy of an interpolating function in Mathematica?

Yes, you can adjust the accuracy of an interpolating function in Mathematica by using the "AccuracyGoal" and "PrecisionGoal" options when creating the function. These options allow you to specify the desired level of accuracy for the function.

4. How can I plot an interpolating function in Mathematica?

To plot an interpolating function in Mathematica, you can use the command "Plot[function, {x, xmin, xmax}]" where "function" is the interpolating function you created and "xmin" and "xmax" are the minimum and maximum values of the x-axis. You can also add options to customize the appearance of the plot.

5. Is it possible to combine multiple interpolating functions in Mathematica?

Yes, it is possible to combine multiple interpolating functions in Mathematica by using the "Piecewise" command. This allows you to specify different regions where each interpolating function will be used. You can also use the "InterpolationOrder" option to adjust the smoothness of the combined function.