Interpolating function with monotonic decresing first derivative

Hello, everyone.

I want to find an interpolating function with monotonic decreasing first derivative as shown in the figure.

The black points are the data and the red line is the interpolating function I want to get.

The only condition of interpolating function is: dY/dX should monotonic decreasing .

Is their any interpolating function and solve this problem in MATLAB??

Thanks for any helpful ideas.

[Jan]

There is an infinite number of interpolating functions matching these points and the condition. Is dy/dx < 0 wanted globally or only in the interpolated interval?

[Bruno Luong]

"dY/dX should monotonic decreasing "

Your cannot with this data dY/dx is increases in some discrete points so you can never get dY/dx decreases.

Now if you mistake "dY/dx decrease" for "Y decreases" of "dY/dx < 0", that is possible.

Signed by Mr pedantic

[Jan]

I missed you, Mr. exact Bruno. Maybe "decreasing derivative" is a weak formulation only, maybe it is the actual problem.

[Dimitris Kalogiros]

I think , that "red" function of the given graph, has an increasing derivative. I wonder whether the restriction is: dy/dx should be negative

[Kim Jeong Min]

I am sorry to cause confusion.

Yes, dY/dX itself should increasing and dY/dX is a negative value globally.

[Torsten]

Maybe Y = a*exp(-b*X) with a,b to be determined is a good choice for the function.

[Bruno Luong]

For fitting or interpolating?

[Torsten]

ok, fitting ...

[Kim Jeong Min]

The purpose of this project is making discontinuous data become continuous. So, I think both options are acceptable.

Answer 1

[Bruno Luong]

You can use PCHIP, either in the toolbox or as option of INTERP1 for shape-preserving interpolation.

For fitting you might take a look at my BSFK tool or John d'Errico SLM.

[Kim Jeong Min]

Thank you for your solution. I realized the interpolating method must pass the data which is not I want. I think I have to try fitting procedure through your opinion.