System of Equation

Types

Functions

LUSE_ENGR701_704_NumericalMethods.SystemOfEquations.conjugate_gradientFunction
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.

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LUSE_ENGR701_704_NumericalMethods.solveMethod
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).

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Index