# Questions tagged [iterative-method]

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.

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### What are the advantages and disadvantages of using norm error control in the MATLAB ODE suit?

In MATLAB's ODE suit, there seem to be two basic methods of controlling the Local Truncation Error (LTE) of the ODE which the user can choose from, namely: The absolute error control (default), ...
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### When will the Orthomin/CG iteration fails

I know that the the Conjugate Gradient iteration fails when $0\in \mathcal {W}(A^{H})$, which means there's a complex vector $x+iy$ such that $(x+iy)^{T}A^{H}(x+iy)=0$. I wonder how to derive a real ...
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### How to derive the simplified Newton iteration in the TR-BDF2 ODE integration scheme

The Problem The TR-BDF2 explained in this paper [1], is quite a popular numerical scheme used to integrate $\dot{y} = f(t,y)$, consistent of the following two stages: \begin{align} y_{n+\gamma} &...
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1 vote
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### How can I color my Mandelbrot set like this?

I have a background image of a fractal on my phone that I would like in a higher resolution with super sampling, and decided to write my own program for it. I've got down rendering a Mandelbrot set, ...
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### Is it possible to predict solution oscillation before solving the system by looking at coefficient matrix?

Question When it is about solving a system of equations, is it possible to predict that whether high-frequency noise (e.g. checker-boarding) is likely to appear in the converged solution by looking at ...
• 235
166 views

### Project to nearest point on convex polytope

I have a point $y \in \mathbb{R}^d$ and a convex polytope $\mathcal{P}$ given as the intersection of half-spaces: \mathcal{P} = \{x \in \mathbb{R}^d \mid a_1 \cdot x \le b_1, \dots, a_n \cdot x \le ...
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### Preconditioning the $[1 \quad-2 \quad 1]$ Finite Difference matrix

Let $A$ be the well known tridiagonal matrix coming from the 1D Finite difference discretization of the Laplacian, with stencil $\frac{[1 \quad-2 \quad 1]}{h^2}$. The system $Ax = b$ is very large, so ...
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### Is there an iterative solver for dense matrices with possible zero diagonal entries?

Is there an iterative solver that can handle potentially zero entries on the central diagonal? I am implementing a polynomial fitting algorithm (up to $10^{th}$-order) and my matrix is a "...
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1 vote
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### 2D heat equation in both steady state and Transient state using iterative solvers

While solving a 2D heat equation in both steady-state and Transient state using iterative solvers like Jacobi, Gauss seidel, SOR. Should the answers, I mean the converged results of Temperature ...
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### Without positive definiteness, does an iterative solver work?

Question Does lacking positive definiteness of the matrix of coefficients in a system of equations, make using iterative solvers impractical? Description Using the finite volume method, I have ...
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I have to solve the the problem $u_t+\Delta^2u=f(u)$, where $f(u)$ is non-linear, using domain-decomposition method. My approach is first using fixed point iteration on mixed form i.e to say \$u^{k+1}...