- Gauss Backward Interpolation Formula
- Gauss Backward Interpolation Formula C Programming
- Double Interpolation Formula
- Interpolation Formula Excel
- Interpolation
Working C C++ Source code program for Gauss jordan method for finding inverse matrix /***** Gauss Jordan method for inverse matr. Understanding Dependency Injection and its Importance, A tutorial Any application is composed with many classes that collaborate each-other to perform some useful stuff. /*program for newton backward difference formula for interpolation */ #include #include #include void main(). C program for newton forward difference formula fo. C program for newton backward difference formula f. C program for lagrange's interpolation formula; c program for gauss elimination method.
The above gaussian eleimination algorithm works fine on NxN matrices. But I need it to work on NxM matrix. Can anyone help me to do it? I am not very good at maths. I got this code on some website and i am stuck at it.
Daniel KutikGauss Backward Interpolation Formula
3 Answers
- (optional) Understand this. Do some examples on paper.
- Don't write code for Gaussian elimination yourself. Without some care, the naive gauss pivoting is unstable. You have to scale the lines and take care of pivoting with the greatest element, a starting point is there. Note that this advice holds for most linear algebra algorithms.
- If you want to solve systems of equations, LU decomposition, QR decomposition (stabler than LU, but slower), Cholesky decomposition (in the case the system is symmetric) or SVD (in the case the system is not square) are almost always better choices. Gaussian elimination is best for computing determinants however.
- Use the algorithms from LAPACK for the problems which need Gaussian elimination (eg. solving systems, or computing determinants). Really. Don't roll your own. Since you are doing C++, you may be interested in Armadillo which takes care of a lot of things for you.
- If you must roll your own for pedagogical reasons, have a look first at Numerical Recipes, version 3. Version 2 can be found online for free if you're low on budget / have no access to a library.
- As a general advice, don't code algorithms you don't understand.
You just cannot apply Gaussian elimination directly to an NxM problem. If you have more equations than unknowns, the your problem is over-determined and you have no solution, which means you need to use something like the least squares method. Say that you have A*x = b, then instead of having x = inv(A)*b (when N=M), then you have to do x = inv(A^T*A)*A^T*b.
Gauss Backward Interpolation Formula C Programming
In the case where you have less equations then unknowns, then your problem is underdetermined and you have an infinity of solutions. In that case, you either pick one at random (e.g. setting some of the unknowns to an arbitrary value), or you need to use regularization, which means trying adding some extra constraints.
Double Interpolation Formula
You can apply echelon reduction, like in this snippet