A while back I came upon a seemingly not-too-difficult programming exercise: Define a recurrence  by Compute . This isn't too hard to code up, using perhaps a recursive function to represent . With normal double-precision floats, as increases, the result converges neatly toward 100. Super! Unfortunately, 100 is not even close to the right answer. This … Continue reading Muller's Recurrence - roundoff gone wrong →

A while back I came upon a seemingly not-too-difficult programming exercise: Define a recurrence \(x_n\) by $$f(y, z) = 108 - \frac{815 - 1500/z}{y}$$ $$x_0 = 4$$ $$x_1 = 4.25$$ $$x_i = f(x_{i-1}, x_{i-2})$$ Compute \(x_{30}\). This isn’t too hard to code up, using perhaps a recursive function to represent \(x_i\). With normal double-precision floats, as \(i\) increases, the result converges neatly toward 100. Super! Unfortunately, 100 is not even close to the right answer. This recurrence actually [...]

There is a function I need. I know how to write it, but I don’t know if it has a standard name (like map, fold, etc.). It takes one argument — a list of something — and returns a list of 2-tuples of equal length. Each tuple contains one item from the list and the [...]

How computationally expensive are various fundamental floating point mathematical operations?  Here's a quick and dirty benchmark, which, although surely quite naive, seems to capture the rough relative cost of a few operations. Motivation This quarter I am taking a course on numerical linear algebra.  Naturally, we are covering topics like the fundamentals of floating point arithmetic, numerical … Continue reading A simple benchmark of various math operations →

How computationally expensive are various fundamental floating point mathematical operations?  Here’s a quick and dirty benchmark, which, although surely quite naive, seems to capture the rough relative cost of a few operations. Motivation This quarter I am taking a course on numerical linear algebra.  Naturally, we are covering topics like the fundamentals of floating point arithmetic, numerical stability, matrix decompositions, and algorithm analysis. In a few of our assignments, we are tasked with [...]