topic Re: Implementation of Lagrange Interpolation in Mathcad

Implementation of Lagrange Interpolation

JA_9803374 — Thu, 25 Feb 2021 02:18:18 GMT

Hello, I am trying to implement a program where I can find out the "y" value for a given "x" value using Lagrange Interpolation with data points (x,y) like the ones shown below:

The program should use these expressions:

Re: Implementation of Lagrange Interpolation

JXBWk — Thu, 25 Feb 2021 07:31:16 GMT

While interesting what have you got so far? Couldn't see any attached mcad sheet!

Where are the stumbling blocks?

Re: Implementation of Lagrange Interpolation

Werner_E — Thu, 25 Feb 2021 11:20:10 GMT

As this is obviously homework you should show your attempts for a solution. This also would help us to see where you have problems with the handling of Prime so we can help.

If you already derived a solution you may check your function by creating a plot and also check against the built-in "polyfit" function:

Re: Implementation of Lagrange Interpolation

Fred_Kohlhepp — Thu, 25 Feb 2021 13:37:42 GMT

Assuming Werner's right, and this IS homework, you need to show an honest effort (AKA, post your worksheet!)

That said, these were developed (as LaGrange polynomial interpolation functions) using Prime 4.0 Express. Worksheet will be posted upon demonstration of honest effort.

Re: Implementation of Lagrange Interpolation

Werner_E — Thu, 25 Feb 2021 13:43:18 GMT

@Fred_Kohlhepp wrote:

Assuming Werner's right, and this IS homework,

The poster himself labelled his question with "Math Homework" 🙂

Re: Implementation of Lagrange Interpolation

Fred_Kohlhepp — Thu, 25 Feb 2021 13:45:26 GMT

Thereby demonstrating (once again) that you are much more observant than I! 😉

But I still enjoyed the challenge.

Re: Implementation of Lagrange Interpolation

JA_9803374 — Thu, 25 Feb 2021 14:37:25 GMT

This was my original attempt at it. However I realized two things, Mathcad won't simplify the polynomial basis expressions. Secondly, this method is really inefficient as the Lagrange polynomial degree increases. So I stopped trying this method. I figured I could use two loops and the actual expression. However I'm having trouble implementing that.

Re: Implementation of Lagrange Interpolation

Fred_Kohlhepp — Thu, 25 Feb 2021 16:28:18 GMT

It doesn't look like you've put too much thought and effort into this.

However, as promised!

Re: Implementation of Lagrange Interpolation

Werner_E — Thu, 25 Feb 2021 16:48:38 GMT

I agree with you and your version looks so familiar compared to what I had prepared 🙂

Splitting may make it better readable

@JA_9803374

Keep in mind that Freds sheet assumes the default setting for ORIGIN (which is 0). In your sheet you changed ORIGIN to be 1 so you have to slightly modify Freds approach to take that into account.

Re: Implementation of Lagrange Interpolation

JA_9803374 — Thu, 25 Feb 2021 16:58:11 GMT

Thank you guys! I just needed this because I am new to Mathcad programming and I was just unsure how some of the syntax works for the product function and got completely stuck! thanks for helping me get started!