What's all this, then?

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• The Pegasus and related methods for solving equations | What's all this, then?

  In the previous post, we saw that a small change to the method of false position provided much faster convergence, while retaining its bracketing. This was the …

• High precision quadrature with Clenshaw-Curtis | What's all this, then?

  An article by Bailey, Jeybalan and LI, "A comparison of three high-precision quadrature schemes", and available online here, compares Gauss-Legendre …

• Exploring Tanh-Sinh quadrature | What's all this, then?

  As is well known, tanh-sinh quadrature takes an integral \[ \int_{-1}^1f(x)dx \] and uses the substitution \[ x = g(t) = \tanh\left(\frac{\pi}{2}\sinh t\right) …

• Tschirnhausen transformations and the quartic | What's all this, then?

  Here we show how a Tschirnhausen transformation can be used to solve a quartic equation. The steps are: Ensure the quartic is missing the cubic term, and its …

• About this blog | What's all this, then?

  This is the newest version of my "Numbers and Shapes" blog, containing material on elementary mathematics, mathematics education, software, and …

• Runge's phenomenon in Geogebra | What's all this, then?

  Runge's phenomenon says roughly that a polynomial through equally spaced points over an interval will wobble a lot near the ends. Runge demonstrated this by …