# Give me a fun problem related to numerical methods.

I hope that this doesnt violate the rules since I need a problem instead of an answer.

We have to make our own problem and present it in the class. First course in numerical methods using MatLab.

My initial idea: A function gets n random coordinates in the two-dimensional world [x,y] + a starting coordinate and a destination coordinate. The function then returns an array of coordinates which represent the shortest path between the start and destination. To make it harder add one more dimensions or even more.

However I do need some other fun problem to solve. Thank you.

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"Fun" is a wide saying... How about (mutil-dimensional) curve fitting? – AlexR Oct 16 '13 at 20:47
Solving your first problem using simulated annealing and playing with heat could be fun... – Raymond Manzoni Oct 16 '13 at 22:13

## 2 Answers

Calculate the log factorial function, precisely, with arguments up to the limit of Matlab's ability to express the results.

Look up some quantum mechanical wave equations, and solve them (yeah, way over my head).

Without using the ones Matlab provides, write some routines to solve matrix equations, avoiding instability pitfalls.

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Newton iteration to find the root of some function. Decide whether there is a root at all. Consider conditions, which are good initial guesses and what not - perhaps precondition with bisection or something stable.

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