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On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization (1998) [comparison of Steihaug and dogleg algorithms, as discussed in these lecture notes]

This is the key reference: G.M. Korpelevich, "The extragradient method for finding saddle points and other problems." Ekonomika i Matematicheskie Metody 12 (1976): 747-756. I have not found this arti …

You can't go wrong if you follow Numerical Recipes. Chapter 18.2 has the code for the Volterra integral equation of the second kind. Here is the book itself, there may also be downloadable code online …

Antilimits are used to apply the methods of sequence transformations to divergent series. There is no unique definition, but typically if the sum $\sum_{n}a_n(x)$ converges to some function $f(x)$ for …

Global convergence of Newton's method on an interval, Lars Thorlund-Petersen (2004). Global convergence of Newton's method is considered in the strong sense of convergence for any initial value …

The OP asks for a "reputable source", I would think that Press and Teukolsky's Numerical Recipes [section 5.7 in The Book] qualifies as such. As they explain, if you approximate $f'(x)\approx h^{-1}[f …

Since $\ln x = - \ln(1/x)$, to evaluate the logarithm near zero is equivalent to evaluating it for large argument. You can then use the result $$\ln y=\frac{\pi}{2a}\left(1+{\cal O}(y^{-2})\right),$$ …

In the field of hydrodynamics the first calculation by a human computer was carried out around 1920 for a project to transform an open sea into a closed lake, with the aim to protect Holland from floo …

An easy and reliable way to share code is via Zenodo --- works much like arXiv, you get a DOI, can update your files, and it's free. We use it regularly to document computer simulations in physics, I …

The maximum $x_n$ of $$f_n(x):=e^{-1/x}\Bigl(1+\frac{1}{n^2 x^n} \Bigr)$$ is the smallest solution in $(0,1)$ of the equation $$x=n x^n+\frac{1}{n}.$$ For $n\gg 1$ this gives $x_n\rightarrow 1/n$. The …

From what I read in the description of INTLAB (a Matlab/Octave "Interval Laboratory"), it has some of the desired capabilities, including gamma, erf and erfc functions, integration of univariate funct …

there is a very large literature, you could start for example from a textbook; an overview of numerical methods is given here: In this paper, we present a critical comparison of the suitability of …

Well, the obvious thing to test first is whether for $d=1$, $\sigma=4$ your solution conserves the $L^2$ norm under the scaling transformation $\psi(x,t)\mapsto L^{-1/2}\psi(x/L,t/L^4)$. For other val …

A well-balanced and asymptotic-preserving scheme for the one-dimensional linear Dirac equation (2014) treats the effect of spin in a probability conserving way, both in the relativistic (Dirac) and no …

it's jargon for a function of the form $$y(x)=e^{a(x-x_0)}[b(x-x_0)+c]$$ where the constants $a,b,c$ are determined such that $y(x)$ osculates the function $f(x)$ you are fitting to at $x=x_0$: $$y(x …