Fitting Curve With an Inverse Which Fits a Polynomial

Question

Ephraim Bryski 2020-10-5

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/605245-fitting-curve-with-an-inverse-which-fits-a-polynomial

评论： Ameer Hamza 2020-10-5

Hi. I have 8 data points with x and y values. I would like to input new y values and interpolate x values.

I am able to input new x values and interpolate y values. I can fit the points with a sixth order polynomial for y vs. x which is valid in the range. However, I cannot fit a polynomial for x vs. y

One approach is to solve the polynomial for each y value; however, I have thousands of y values I want to interpolate for, so it would be extremely computationally intensive.

Does anyone know a faster approach? Thanks!

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Ameer Hamza 2020-10-5

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/605245-fitting-curve-with-an-inverse-which-fits-a-polynomial#answer_505372

编辑：Ameer Hamza 2020-10-5

在 MATLAB Online 中打开

The inverse of a polynomial is not a polynomial, so you cannot simply interpolate the inverse function. Following shows two approaches

1) fzero()

x = linspace(0, 2, 8);
y = 5*x.^6 + 3*x.^5; % y varies from 0 to 416.
pf = polyfit(x, y, 6);
y_pred = @(x) polyval(pf, x);
% find x, when y = 100;
y_val = 100;
x_val = fzero(@(x) y_pred(x)-y_val, rand);

2) Polynomial root finding. This method gives all possible solutions

x = linspace(0, 2, 8);
y = 5*x.^6 + 3*x.^5; % y varies from 0 to 416.
pf = polyfit(x, y, 6);
% find x, when y = 100;
y_val = 100;
pf(end) = pf(end)-y_val;
x_vals = roots(pf);
x_vals = x_vals(imag(x_vals)==0); % if you only want real roots.