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Carl, in honor of Carl Jacobi and Carl Friedrich Gauss, is a program written in python that implements two of the best known iterative methods for solving sparse linear systems: Jacobi method and Gauss-Seidel method. According to algebraic theory, solving a linear system can be taked back to the problem of finding the vector x that satisfies the relation Ax = b where A, b are parametrs given in input, called respectively - A coefficient matrix: describe a particular problem. The files containing matrices can be download from http://math.nist.gov/MatrixMarket, a popular repositories that contain a wide collection of matrices. Once download a .mtx file, put it in dataset folder - b vector of known terms: for our purpose b is initialized with a vector filled with 1 A detailed discussion of the iterative methods can be found in the following link: http://www-users.cs.umn.edu/~saad/books.html https://en.wikipedia.org/wiki/Iterative_method In order to run the program you need to use the syntax python carl.py <mtx file> [gauss|jacobi] <MAXITER> <TOLL> For default MAXITER is 100 and TOLL is 1e-4 Examples: python carl.py pde225.mtx gauss python carl.py pde225.mtx jacobi 2000 python carl.py pde225.mtx jacobi 3000 1e-8
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A python tool, that implements iterative methods for solving sparse linear systems
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