Your problem is to couple the Newton-Raphson and the Gauss-Seidel solvers. Use and abuse MATLAB syntax to deal with matrices and vectors.Not only it is much slower, it cannot solve all numerical problems. Avoid at all costs the use of symbolic variables. First of all, notice that both the Newton-Raphson method and the Gauss-Seidel method are numerical methods to solve system of equations.You are on the right track, but there are a few things we could improve in your code: I have coded the NR method before but only with 1 variable so I do not understand how to transfer this logic into this code. Basically, I am not sure how to incorporate Newton Raphson into it. I was told to do a guess of for the linear equation and for the nonlinear equation. Right now, it outputs an iteration of 0 once I got rid of the errors. I have tried to code this, and I believe that the matrices are correct, and I think that the Gauss Seidel function is correct, but I am extremely confused on how to update the guess properly. First, I would like to know if my logic is right, and a pseduocode for this set up would be very helpful. My main confusion comes from how to accurately set this up together and with two different variables. I have before coded the Newton Raphson and Gauss Seidel methods before but separately. When the error is smaller than the tolerance, the values are reported. Each iteration has an error between the old and new guess.I will then plug in that updated x, find another h, and continue that process. First plug in my intital guesses for x into the first and last matrix, and then every time I solve for H, i'll add that stepsize to the previous guess of x to create a new x.
Transfer the system so we have =, where H is what i am solving for. Linearize the system by finding the derivative of the equations and put into matrix.#LnormInf corresponds to the absolute value of the greatest element of the vector.I need help figuring out how to incorporate Newton Raphson and Gauss Seidel methods to solve a nonlinear system of equations in Matlab.
Print ("The solution vector in iteration", iter1, "is:", x)
def gauss_seidel(A, b, tolerance, max_iterations, x): Instead I created my own little function that with the help of a permutation matrix as seen in another answer of mine permutation matrix will produce the solution (x vector) for any square matrix, including those with zeros on the diagonal. I know this is old but, I haven't found any pre existing library in python for gauss - seidel.
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