# Category Archives: numerical algorithms

## Phase Plane plots of COVID-19 deaths *with uncertainties*

I. Introduction. It’s time to fulfill the promise made in “Phase plane plots of COVID-19 deaths“, a blog post from 2nd May 2020, and produce the same with uncertainty clouds about the functional trajectories(*). To begin, here are some assumptions … Continue reading

## Calculating Derivatives from Random Forests

(Comment on prediction intervals for random forests, and links to a paper.) (Edits to repair smudges, 2020-06-28, about 0945 EDT. Closing comment, 2020-06-30, 1450 EDT.) There are lots of ways of learning about mathematical constructs, even about actual machines. One … Continue reading

## JIGSAW-GEO v1.0

See: D. Engwirda, 2017: JIGSAW-GEO (1.0): Locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere, Geosci. Model Dev., 10, 2117-2140, doi:10.5194/gmd-10-2117-2017 and a general description at NASA. The figure below is copied from there.

## Stream flow and P-splines: Using built-in estimates for smoothing

Mother Brook in Dedham Massachusetts was the first man-made canal in the United States. Dug in 1639, it connects the Charles River at Dedham, to the Neponset River in the Hyde Park section of Boston. It was originally an important … Continue reading

## Series, symmetrized Normalized Compressed Divergences and their logit transforms

(Major update on 11th January 2019. Minor update on 16th January 2019.) On comparing things The idea of a calculating a distance between series for various purposes has received scholarly attention for quite some time. The most common application is … Continue reading

## The Johnson-Lindenstrauss Lemma, and the paradoxical power of random linear operators. Part 1.

Updated, 2018-12-04 I’ll be discussing the ramifications of: William B. Johnson and Joram Lindenstrauss, “Extensions of Lipschitz mappings into a Hilbert space, Contemporary Mathematics, 26:189–206, 1984. for several posts here. Some introduction and links to proofs and explications will be … Continue reading

## Sampling: Rejection, Reservoir, and Slice

An article by Suilou Huang for catatrophe modeler AIR-WorldWide of Boston about rejection sampling in CAT modeling got me thinking about pulling together some notes about sampling algorithms of various kinds. There are, of course, books written about this subject, … Continue reading

## Fast means, fast moments (originally devised 1984)

(Updated 4th December 2018.) There are many devices available for making numerical calculations fast. Modern datasets and computational problems apply stylized architectures, and use approaches to problems including special algorithms for just calculating dominant eigenvectors or using non-classical statistical mechanisms … Continue reading

## When linear systems can’t be solved by linear means

Linear systems of equations and their solution form the cornerstone of much Engineering and Science. Linear algebra is a paragon of Mathematics in the sense that its theory is what mathematicians try to emulate when they develop theory for many … Continue reading

## forecast for 27th March 2018

Today is the 21st of March, 2018. We are supposed to get our fourth nor’easter tomorrow this late Winter, and the third nor’easter in nearly as many weeks. ECMWF hosted, in this incarnation, at the Meteocentre UQAM in Montreal created … Continue reading

## on nonlinear dynamics of hordes of people

I spent a bit of last week at a symposium honoring the work of Charney and Lorenz in fluid dynamics. I am no serious student of fluid dynamics. I have a friend, Klaus, an engineer, who is, and makes a … Continue reading

## What are the odds of net zero?

What’s the Question? A question was posed by a colleague a couple of months ago: What are the odds of a stock closing at the same price it opened? I found the question interesting, because, at first, it appeared to … Continue reading

## A new feature: Technical publications of the week

I’m beginning a new style of column, called technical publications of the week. While I can’t promise these will be weekly, I will, from time to time, highlight technical publications I’ve recently read which I consider to be noteworthy. I … Continue reading