Tag: Numerical Analysis

Analytics
Rick Wicklin 0
The geometry of Jacobi's method

A colleague remarked that my recent article about using Jacobi's iterative method for solving a linear system of equations "seems like magic." Specifically, it seems like magic that you can solve a certain class of linear systems by using only matrix multiplication. For any initial guess, the iteration converges to

Analytics | Learn SAS | Programming Tips
Rick Wicklin 0
A test for monotonic sequences and functions

Monotonic transformations occur frequently in math and statistics. Analysts use monotonic transformations to transform variable values, with Tukey's ladder of transformations and the Box-Cox transformations being familiar examples. Monotonic distributions figure prominently in probability theory because the cumulative distribution is a monotonic increasing function. For a continuous distribution that is

Analytics | Programming Tips
Rick Wicklin 0
Finite-difference derivatives of vector-valued functions

I previously showed how to use SAS to compute finite-difference derivatives for smooth scalar-valued functions of several variables. You can use the NLPFDD subroutine in SAS/IML software to approximate the gradient vector (first derivatives) and the Hessian matrix (second derivatives). The computation uses finite-difference derivatives to approximate the derivatives. The

Analytics | Programming Tips
Rick Wicklin 0
Finite-difference derivatives in SAS

Many applications in mathematics and statistics require the numerical computation of the derivatives of smooth multivariate functions. For simple algebraic and trigonometric functions, you often can write down expressions for the first and second partial derivatives. However, for complicated functions, the formulas can get unwieldy (and some applications do not

Programming Tips
Rick Wicklin 0
Pi and products

This is my Pi Day post for 2021. Every year on March 14th (written 3/14 in the US), geeky mathematicians and their friends celebrate "all things pi-related" because 3.14 is the three-decimal approximation to pi. Most years I write about lower-case pi (π), which is the ratio of a circle's

Programming Tips
Rick Wicklin 0
Trap and map: Trapping invalid values

Finite-precision computations can be tricky. You might know, mathematically, that a certain result must be non-negative or must be within a certain interval. However, when you actually compute that result on a computer that uses finite-precision, you might observe that the value is slightly negative or slightly outside of the

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