How do Physicists Consider Interpolation?

[Iwonderaboutthings]

How do Physicists Consider Interpolation?

 

The following link shows a statistics method on dynamic responses to time.

 

Here is a link:

 

Applications of Imaginary Numbers in the Real World

 

http://www.picomonster.com/complex-numbers-meet-dynamic-systems-lesson-2/

 

 

 

However, Do Physicists Consider Interpolation in this link above?

 

 

My personal issues with Interpolation:

 

In 3d animation using my computer it uses curves for editing motion of the game, characters and etc.

 

I have 3 options as per animation Interpolation:

 

 

1:Constant

 

2:Linear

 

3:Bezier

 

 

 

I "always" choose "Linear" otherwise there will be a delay in the animation from the original "real time" recording of my animation.

 

 

What does this have to do with science?

 

 

 

I have noticed the "Linear" word used in many math styles Linear Algebra being one of them.,

 

Linear Algebra

http://en.wikipedia.org/wiki/Linear_algebra

 

 

I was also wondering if this had anything to do with:

 

Rest Mass

Constant Velocity

And Velocity

 

 

Thanks In Advance,

Edited July 20, 2013 by Iwonderaboutthings

[swansont]

This is an open-ended question and impossible to answer fully. It depends on the situation, and I don't see what you want to interpolate in your link.

 

One thing physicist do is expand expressions in some kind of series, often a Taylor series. Then it's a matter of determining if a linear expression gives sufficient precision. If not, you keep adding higher-order terms until you do. It works for extrapolation and interpolation.

 

Another way is curve-fitting, if your data are supposed to follow some expression and you have free parameters. You find the best fit and since you have a continuous function you can interpolate to find any answer.

[studiot]

There are too many questions in the original post.

 

As a start I suggest you get hold of the difference between interpolation and extrapolation and why the latter is a more risky method.

 

Both methods are ways of obtaining the value of some function at points you have not measured or do not have tabulated data for and cannot calculate exactly.

Edited July 20, 2013 by studiot

[Iwonderaboutthings]

There are too many questions in the original post.

 

As a start I suggest you get hold of the difference between interpolation and extrapolation and why the latter is a more risky method.

 

Both methods are ways of obtaining the value of some function at points you have not measured or do not have tabulated data for and cannot calculate exactly.

You are very correct I had no idea about interpolation and extrapolation , from your reply it is extrapolation that I am looking for.

One question here please, is extrapolation similar in a sense to the Wave Function used in QM??

 

Thanks

[swansont]

You are very correct I had no idea about interpolation and extrapolation, from your reply it is extrapolation that I am looking for.

One question here please, is extrapolation similar in a sense to the Wave Function used in QM??

Similar? No, not in any reasonable sense of the word. It's like comparing a noun and a verb (is running similar to a stick?)— it makes no sense to make the comparison.

[studiot]

 

One question here please, is extrapolation similar in a sense to the Wave Function used in QM??

 

Extrapolation means going beyond what you know to guess at what you don't know.

 

This can lead to your guess being wildly wrong, as in the above. The Wave Function is in no sense an extrapolation.

 

Interpolation means bracketing what you don't know between things you do know in the hope that your guess will be closer.

It can also be very inaccurate, but it can yield useful, even good results as well.

[Iwonderaboutthings]

 

Extrapolation means going beyond what you know to guess at what you don't know.

 

This can lead to your guess being wildly wrong, as in the above. The Wave Function is in no sense an extrapolation.

 

Interpolation means bracketing what you don't know between things you do know in the hope that your guess will be closer.

It can also be very inaccurate, but it can yield useful, even good results as well.

I agree thanks

Similar? No, not in any reasonable sense of the word. It's like comparing a noun and a verb (is running similar to a stick?)— it makes no sense to make the comparison.

Yes very true, gonna try my best to fully understand the wave function, but those " symbols' are something awful to understand, wish there was an easier way...