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My professor said for our final we would have to solve linear systems by hand on our final. Some of our questions for interpolation and finding splines involve large 6x6 or 12x12 matrices. What is the best way for solving these by hand?

LU Decomposition is handy, not sure if it's the best method by hand, though.

Neurax
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  • What tricks have you learned in the semester? I'd hazard a guess that if it seems tedious, there's an easier way? (Unless he really wants to test how well you do arithmetic, in which case all bets are off.) – John Dec 12 '13 at 21:38
  • @John I can't imagine that arithmetic is important. MatLab can very easily solve these systems, and the more important piece seems to be getting TO the linear system, but he asked for solutions to the practice questions by hand.. Strange. – Neurax Dec 12 '13 at 21:42
  • See my Solution 2, http://math.stackexchange.com/questions/485513/what-are-pivot-numbers-in-lu-decomposition-please-explain-me-in-an-example, which can be very quick. – Amzoti Dec 12 '13 at 22:24

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See my comments on your other question about spline interpolation. As I explained there, the matrices and systems of equations that occur in constructing splines are special, because they are banded. So, you can solve them using elementary elimination methods. You don't need to use general-purpose methods like LU decomposition.

I suspect that your teacher is asking you to solve these problems by hand so that you see this banded structure and you understand how much it simplifies the problem. If you do polynomial interpolation (as opposed to spline interpolation), then you again have to solve linear systems, but they are not banded. Doing a few examples by hand will help you appreciate the difference. The brute-force approach using Matlab hides all this.

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bubba
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