Did you know that you can get SAS to compute symbolic (analytical) derivatives of simple functions, including applying the product rule, quotient rule, and chain rule? SAS can form the symbolic derivatives of single-variable functions and partial derivatives of multivariable functions. Furthermore, the derivatives are output in a form that

## Tag: **Numerical Analysis**

The singular value decomposition (SVD) could be called the "billion-dollar algorithm" since it provides the mathematical basis for many modern algorithms in data science, including text mining, recommender systems (think Netflix and Amazon), image processing, and classification problems. Although the SVD was mathematically discovered in the late 1800s, computers have

All statisticians are familiar with the classical arithmetic mean. Some statisticians are also familiar with the geometric mean. Whereas the arithmetic mean of n numbers is the sum divided by n, the geometric mean of n nonnegative numbers is the n_th root of the product of the numbers. The geometric

A SAS customer asked, "I computed the eigenvectors of a matrix in SAS and in another software package. I got different answers? How do I know which answer is correct?" I've been asked variations of this question dozens of times. The answer is usually "both answers are correct." The mathematical

Monte Carlo techniques have many applications, but a primary application is to approximate the probability that some event occurs. The idea is to simulate data from the population and count the proportion of times that the event occurs in the simulated data. For continuous univariate distributions, the probability of an

At a conference last week, a presenter showed SAS statements that compute the logarithm of a probability density function (PDF). The log-PDF is a a common computation because it occurs when maximizing the log-likelihood function. The presenter computed the expression in SAS by using an expression that looked like y

This article describes how you can evaluate the Lambert W function in SAS/IML software. The Lambert W function is defined implicitly: given a real value x, the function's value w = W(x) is the value of w that satisfies the equation w exp(w) = x. Thus W is the inverse

Edmond Halley (1656-1742) is best known for computing the orbit and predicting the return of the short-period comet that bears his name. However, like many scientists of his era, he was involved in a variety of mathematical and scientific activities. One of his mathematical contributions is a numerical method for

I was eleven years old when I first saw Newton's method. No, I didn't go to a school for geniuses. I didn't even know it was Newton's method until decades later. However, in sixth grade I learned an iterative algorithm that taught me (almost) everything I need to know about

Statistical programmers often need to evaluate complicated expressions that contain square roots, logarithms, and other functions whose domain is restricted. Similarly, you might need to evaluate a rational expression in which the denominator of the expression can be zero. In these cases, it is important to avoid evaluating a function