System of Equation

SystemOfEquation(A, b, N, tol)

Solve a linear system of equations (SOE): $\mathbf{A}\vec{x} = \vec{b}$.

conjugate_gradient(SOE, x[, C])

Use initial guess vector, x and (if desired) pre-conditioning matrix, C to solve SOE.

Is best suited for large, sparse matrices. If pre-conditioned, can solve in $\sqrt{n}$ iterations. More computationally expensive than gaussian_elimination for smaller systems.

gaussian_elimination(SOE)

Directly find the solution to linear SOE by Gaussian Elimination with Back Substitution.

steepest_descent(SOE, x)

Approximate solution to SOE with initial guess vector, x.

solve(SOE::SystemOfEquation[; method=:gaussian_elimination, x=nothing, C=nothing])

Solve $\mathbf{A}\vec{x} = \vec{b}$ according to method ∈ {:gaussian_elimination (default), :steepest_descent, :conjugate_gradient}.

Each method has an equivalent convenience function. E.g. solve(SOE; method=:gaussian_elimination) ≡ gaussian_elimination(SOE).