def METHOD_NAME(solved_2x2_block_symmetric_toeplitz_problem):
    A, x_ref, b = solved_2x2_block_symmetric_toeplitz_problem
    linear_solver = LUSolverWithCache()
    x = linear_solver.solve(A, b)
    assert np.allclose(x, x_ref, rtol=1e-10)
    x = linear_solver.solve(A, b)  # Should use cache
    assert np.allclose(x, x_ref, rtol=1e-10)