Clueless Fundatma

Consider the problem described in this StackOverFlow post . You have a function with certain smoothness properties that are apparent on a lo...

Dimension reduction is an important problem in the era of big data. SVD is a classic method for obtaining low-rank approximations of data. ...

A new (to me) python library for easily computing families of orthogonal polynomials. Getting standard (generalized) Gauss quadrature sc...

Given N equispaced data-points \(F_i = F(t = i \Delta t)\), where \(i = 0, 1, ..., N-1\), the Prony method can be used to fit a sum of m d...

For convenience, here is a link to the three blogs in this series in one place. 1. A technique for solving the problem in a special cas...

In a previous post, I asked the question if the method described here can be used with non-Gaussian distributions. Let us explore that b...

In the previous blog post, we saw a special example in which we were able to sample random variables from a joint 2D-Gaussian distribution...

Consider two dependent random variables, \(y_1\) and \(y_2\), with a correlation coefficient \(\rho\). Suppose you are given the marginal...

A plot of log(x) looks something like the following: As x decreases to zero log(x) approaches negative infinity. For negative values o...

Let us  try to explore the structure of an IVP graphically by considering a specific example:\[\dfrac{dy}{dt} = y - y^2, \quad \quad \quad ...

The curve_fit function from scipy.optimize offers a simple interface to perform unconstrained non-linear least-squares fitting. It use...

In a recent post, I discussed the use of F2PY for speeding up parts of python code. The radial distribution function (RDF) or the pair ...

Python is notoriously slow with loops. One of the many ways to speed things up is to incorporate subroutines written in C or Fortran into P...

I'd written about block averaging to estimate error bars from correlated time-series in a couple of blog posts nearly three years ago. ...

Our department, Scientific Computing, is highly interdisciplinary, and we get graduate students from very different backgrounds. Here ...

In 1964, Abraham Savitzky and Marcel Golay published a paper "Smoothing and differentiation of data by simplified least squares proce...

I was recently pondering about the area of intersection of two ellipses. That is, given two ellipses with known shapes (semi-major and mino...

Butcher's " A History of Runge-Kutta Methods " contains a beautiful account of the early days of this now ubiquitous method f...

When Warren Buffett was asked how he would ask his wife to manage their money after he was gone, his advice was simple . My advice to th...

In scientific computing or numerical analysis, truncation and roundoff errors pop up all over the place. In some operations the former do...