A method which produces a sequence of numerical approximations which converges (provided technical conditions are satisfied) to the solution of a problem, generally through repeated applications of some procedure. Examples include Newton's method for root finding, and Jacobi iteration for matrix-vector solves.
Questions tagged [iterative-method]
299 questions
7
votes
2 answers
Hartree Fock iteration problem
I am writing a program to compute the ground state energy for any closed shell atom using Hartree Fock Roothaan method, with GTO basis. The code works for the simplest case, the helium, but it fails with beryllium (z=4).
I understand that I have two…
Cheong
6
votes
3 answers
Newton's method for a given polynomial
Let $f(x)=\frac{1}{5}x^5+\frac{1}{3}x^3+x-1$
Show that $f$ has only one zero $r$ in interval $(0,1)$
To find approximation of $r$ we apply Newton's method $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$. Show that for every $x_0\in(0,1)$ this method…
xan
- 315
- 1
- 4
6
votes
1 answer
Numerical iterative method, estimating error
Given iterative method: $x_{n+1}=0.7\sin x_n +5 = \phi(x_n)$ for finding solution for $x=0.7\sin x +5$, I want to estimate $|e_6|=|x_6-r|$ as good as possible, with $x_0=5$, where $r$ is exact solution. This method obviously converges, because…
xan
- 315
- 1
- 4
2
votes
2 answers
Does iterative method work for singular consistent linear system Ax=b?
Recently, I have been studied iterative methods for large sparse linear system Ax=b, where A is nonsingular, so there is a unique solution x. And the stopping criterion is usually chosen with norm(b-Ax_k)/norm(b)< tol (may 1e-6).
But some situations…
Happy
- 961
- 4
- 11
1
vote
0 answers
BicgStab is not able to solve while Jacobi or GaussSeidel Methods can
I am trying to solve the 2D laplace equation,
$\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0; \qquad 0 \lt x \lt 1, \quad0 \lt y \lt 1$
Subjected to the boundary conditions,
${\frac{d T}{d x}}|_{x=0,y}=0;$
${\frac{d…
Null1011
- 11
- 2