Emacs-related articles on Nick Higham's blog.
See also the interesting "What Is" series of articles, mostly on numerical linear algebra.

Software that aims to provide an easy to use (hopefully) universal blackbox for solving polynomials and secular equations.

Among its features you can find:
- Arbitrary precision approximation.
- Guaranteed inclusion radii for the results.
- Exploiting of polynomial structures: it can take advantage of sparsity as well as coefficients in a particular domain (i.e. integers or rationals).

It can be specialized for specific classes of polynomials. As an example, see the roots of the Mandelbrot polynomial of degree 2.097.151 computed in about 10 days on a dual Xeon server.

If you use MPSolve in your research, please cite it as follows:
Bini, Dario A., Fiorentino, Giuseppe, Design, analysis, and implementation of a multiprecision polynomial rootfinder. Numerical Algorithms 23.2-3 (2000): 127-173.
Bini, Dario A., and Robol, Leonardo. Solving secular and polynomial equations: A multiprecision algorithm. Journal of Computational and Applied Mathematics 272 (2014): 276-292.
Found via https://en.m.wikipedia.org/wiki/Aberth_method and https://en.m.wikipedia.org/wiki/MPSolve
See also the GitHub repository http://github.com/robol/MPSolve.git A simpler implementation of the Ehrich-Aberth-method can be found in https://github.com/robol/ea-roots

The HP 48 object listed below in ->ASC form is a high-performance polynomial root finder. Those of you who remember the HP 71B Math Pac will recognize this as the same as the PROOT command from that Pac; it is in fact the same assembly-language code, given an RPL front end to operate in the HP 48.
Found on https://www.hpmuseum.org/forum/thread-10967-post-160700.html#pid160700
See also http://www.jeffcalc.hp41.eu/emu71/mathrom.html#src for the uncommented source code of PROOT and other functions of the HP71B math pack.

Starlink Cookbook, 2003
Central Laboratory of the Research Councils
Particle Physics & Astronomy Research Council
Somewhat dated guide to numerical computing on Unix. Found via https://en.wikipedia.org/wiki/Numerical_Recipes

Not only older issues of the Numerical Recipes books, but also classics such as
Handbook Abramowitz and Stegun, Handbook of Mathematical Functions (10th corrected printing, 1972)

Bateman, Erdelyi et al. (Bateman Manuscript Project)
Higher Transcendental Functions (vols. 1, 2, and 3)

and
Encyclopaedia Britannica the great 11th Edition (1911)

Found via https://www.hpmuseum.org/forum/thread-16251-post-142741.html#pid142741

Matlab implementation of the Durand-Kerner algorithm to compute the roots of a polynomial.

This is just an example, the site contains a large number of documents written at MIT.

Written by one of the foremost experts in high-performance computing and the inventor of Gustafson's Law, The End of Error: Unum Computing explains a new approach to computer arithmetic: the universal number (unum). The unum encompasses all IEEE floating-point formats as well as fixed-point and exact integer arithmetic. This new number type obtains more accurate answers than floating-point arithmetic yet uses fewer bits in many cases, saving memory, bandwidth, energy, and power.

MIT Photonic Bands (MPB) electromagnetic eigenmode solver Meep finite-difference time-domain simulations Harminv extraction of complex frequencies and amplitudes from time series libctl Scheme/Guile-based scripting of scientific code (used as the interface for MPB and Meep). h5utils visualization of HDF5 data files NLopt nonlinear optimization library implementing many different optimization algorithms Cubature code for adaptive multidimensional integration of vector-valued integrands via the Genz-Malik algorithm. Faddeeva_w code to compute the complex error function (Faddeeva function).

Windows applications or source code for various numerical algorithms, with emphasis on polynomial root finding. Some algorithms can be used via a web interface.