Fitting a Transcendental Equation with Multiple Solutions

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bil 2023-3-15

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https://ww2.mathworks.cn/matlabcentral/answers/1929440-fitting-a-transcendental-equation-with-multiple-solutions

移动：Matt J 2023-3-16

Hey all,

I would like to know if there is a way to fit a transcendental equation with multiple solutions. For example, if I had an equation y = f(x,y) that had multiple solutions and thus multiple outputs y for any given input x, is it possible to fit it to a data set that say, takes the form of a matrix, where each column of the matrix represents the set of outputs y, at a specific value of x.

Hopefully my question makes sense!

Thanks.

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Walter Roberson 2023-3-16

Do I understand correctly that you have a set of x values, and a matrix M of y values with the same number of columns as numel(x), such that M(:,K) is the complete set of y values that are possible for X(K) ? If so are the values in sorted order, or do they "follow" the branches?

Imagine two sine waves of different phases: at some point they cross. Would it be like

.48 .5 .52

.53 .51 .49

where the rows follow the path from the previous row, or would it be like

.48 .5 .49

.53 .51 .52

where the columns are in sorted order?

The difference would be in the code to figure out which branch to interpolate against.

bil 2023-3-16

Hi, the answer to your first question ("Do I understand correctly that you have a set of x values, and a matrix M of y values with the same number of columns as numel(x), such that M(:,K) is the complete set of y values that are possible for X(K) ?") is yes.

For your second question, the answer is that they follow the branches. So the columns would be as in your first example.

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