System of Equation
Types
LUSE_ENGR701_704_NumericalMethods.SystemOfEquations.SystemOfEquation
— TypeSystemOfEquation(A, b, N, tol)
Solve a linear system of equations (SOE): $\mathbf{A}\vec{x} = \vec{b}$.
Functions
LUSE_ENGR701_704_NumericalMethods.SystemOfEquations.conjugate_gradient
— Functionconjugate_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.
LUSE_ENGR701_704_NumericalMethods.SystemOfEquations.gaussian_elimination
— Methodgaussian_elimination(SOE)
Directly find the solution to linear SOE
by Gaussian Elimination with Back Substitution.
LUSE_ENGR701_704_NumericalMethods.SystemOfEquations.steepest_descent
— Methodsteepest_descent(SOE, x)
Approximate solution to SOE
with initial guess vector, x
.
LUSE_ENGR701_704_NumericalMethods.solve
— Methodsolve(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)
.