# Using PETSc to solve Ax=rhs

Hello everyone,
I am trying to reduce the time for solving the system of linear equations: Ax=rhs.
My method is to use factorization provided by “pkg:LinearAlgebra”.
However, I know that if we can use PETSc it will be much faster for the large matrix.
Herein, I give a simple code for illustration by using factorization provided by “pkg:LinearAlgebra”.
Then, if you know how to use “PETSc” in Julia to modify these codes, could you please help me? I appreciate your help.
Thanks a lot.

using LinearAlgebra
n = 10000; # size of matrix
A = 100*rand(n,n); # matrix A
rhs = 5*rand(n); # Right hand side rhs
A_factorized = factorize(Symmetric(A)) # factorize
x = A_factorized\rhs; # Solve

for dense matrices like the one you posted, LinearAlgebra is likely to be optimal as long as you aren’t on a cluster. For large sparse matrices, you likely want to use LinearSolve.jl which, like PETSc, provides krylov methods as well as factorization based methods.

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Dear Smith,