# Questions tagged [convergence]

Questions related to whether the sequence of iterates generated by an iterative method has one or more limit points, and if those limit points have the correct properties.

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### DIIS method to accelerate SCF convergence for stretched geometries

I am implementing from scratch an Hartree-Fock calculation in the STO-3G basis set to perform Born-Oppenheimer molecular dynamics. I have a Restricted Hartree-Fock procedure that can reproduce very ...
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### Does applying the Newton-Raphson iteration for matrix reciprocal refine a matrix inverse from LU/GE?

This is a follow-up to this answer. Suppose you have a possibly very ill-conditioned matrix $A$, and you compute its inverse with LU/GE to get $X_{\text{lu}}\approx A^{-1}$. The Newton-Raphson ...
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### Strange convergence behavior of WENO5 for Hamilton--Jacobi equations

I have the following question. I have a code function that computes right-biased and left-biased approximations of the derivative of a function using WENO5 for Hamilton--Jacobi equations as described ...
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### Dynamic Successive Over/under Relaxation (SOR) with several variables

I am solving a partial differential algebraic equation (PDAE) system which has the following dependent variables: $f=f(X,T)$ and $g=g(T)$, along with a few others My current method for coupling is ...
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### Newton Iteration method convergence

I wrote a Python code which solves a second degree nonlinear differential equation using the Newton iteration method. The code converges to a 2-cycle within 50 or so iterations. The cycle only ...
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### Confused on how Method of Manufactured solutions works?

I am new to computational science and I am trying to wrap my head around how MMS works. I am solving the time independent Helmholtz equation as a simple test of the technique so my starting equation ...
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### Multigrid Reduction In Time Convergence

I am trying to solve a 2D dynamic linear elasticity model parallel in time using Xbraid. The spatial domain is [0,1]x[0,1] and time domain [0,1]. For time integration I am using a backward Euler ...
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### Convergence of Conjugate Gradient Algorithm

I am trying to solve a linear elasticity model using finite element discretization in a rectangle domain [0,1]x[0,1]. For the solution of the the linear system $Ku=F$ I am using the CG algorithm. ...
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I am trying to solve a set of couple ODEs: $V_l(r) - r W_l(r) - f1(r) W_l' = 0\tag 1$ $r^2 h''_l(r) + f2 r h_l'(r) + f3 h_l(r) - f4 U_l(r) = 0 \tag 2$ $\kappa (U_l + h_l) + V_{l+1} + W_{l+1} = 0\... 0answers 108 views ### Hatree-Fock, reasons for convergence/ non-convergence I'm new here so please forgive me if I lack proper stack exchange etiquette. So, I was wondering if anyone here could provide insight on a problem that I am running into with with a Hartree-Fock ... 0answers 119 views ### Getting euclidean distance between vector A and C without anyway of retrieving them when their distances with a common vector B is known Motivation: My plan is to get the overall euclidean distance matrix for all the vectors in N number of dataset. Each dataset is basically an array of n-dimensional points. For e.g: A dataset can be ... 0answers 25 views ### Convergence of the Roothaan-Hall equations Suppose that we are given a time-independent quantum mechanical system whose wavefunction depends on three space coordinates. Let$Fbe the Fock operator of the system. Suppose also that we have a ... 0answers 64 views ### L2 norm optimization problem I have an optimization problem where i need to find an image x, that is very close to x' such that: monitor(x') is valid but monitor(x) is invalid. (output is valid when the neural network output is ... 0answers 38 views ### Devising Convergent Numerical Scheme for PDE I'm currently looking at the PDE \begin{align*} u_t + \left[x(1-y) - (1-x)\right]u_x - (1-y) u_y + (z-xy) u_z = (z-xy) u_{xy} - (1-x)u& \\ \end{align*} with \begin{align*} u(x,y,z,0) = 1& \\ ... 0answers 37 views ### How can the choice of coarsening factor affect Multigrid's convergence? The linear systemAx=b$is coming from the discretization of an elliptic PDE. Multigrid method is used in order to solve it. Suppose$c_0$is the coarsening factor on level 0 and$c_m$the coarsening ... 1answer 107 views ### interface value on the error equation https://www.jstor.org/stable/pdf/2157482.pdf, here I have a problem in last equation of (2.6) in section (2.1). When they are considering error equation on the interface$\Gamma$they get$e_v^{(n)} = ...
I have a nonlinear solver for equation $g= c_1f(x_1,y_1)+c_2f(x_2,y_2)$. Note that $c_1$ is much bigger than $c_2$. So after using Levenberg–Marquardt algorithm, I could only get $x_1$, $y_1$ and \$...