While reviewing a book on numerical analysis, I was reminded of a classic interpolation problem. Suppose you have n pairs of points in the plane: (x1,y1), (x2,y2), ..., (xn,yn), where the first coordinates are distinct. Then you can construct a unique polynomial of degree (at most) n-1 that passes through
A SAS programmer wanted to simulate samples from a family of Beta(a,b) distributions for a simulation study. (Recall that a Beta random variable is bounded with values in the range [0,1].) She wanted to choose the parameters such that the skewness and kurtosis of the distributions varied over range of
I read a journal article in which a researcher used a formula for the probability density function (PDF) of the sample correlation coefficient. The formula was rather complicated, and presented with no citation, so I was curious to learn more. I found the distribution for the correlation coefficient in the
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
In a first course in numerical analysis, students often encounter a simple iterative method for solving a linear system of equations, known as Jacobi's method (or Jacobi's iterative method). Although Jacobi's method is not used much in practice, it is introduced because it is easy to explain, easy to implement,
The collinearity problem is to determine whether three points in the plane lie along a straight line. You can solve this problem by using middle-school algebra. An algebraic solution requires three steps. First, name the points: p, q, and r. Second, find the parametric equation for the line that passes
A previous article shows how to use Monte Carlo simulation to approximate the sampling distribution of the sample mean and sample median. When x ~ N(0,1) are normal data, the sample mean is also normal, and there are simple formulas for the expected value and the standard error of the
Recently I wrote about numerical analysis problem: the accurate computation of log(1+x) when x is close to 0. A naive computation of log(1+x) loses accuracy if you call the LOG function, which is why the SAS language provides the built-in LOG1PX for this computation. In addition, I showed that you
SAS supports a special function for the accurate evaluation of log(1+x) when x is near 0. The LOG1PX function is useful because a naive computation of log(1+x) loses accuracy when x is near 0. This article demonstrates two general approximation techniques that are often used in numerical analysis: the Taylor
The other day I was trying to numerically integrate the function f(x) = sin(x)/x on the domain [0,∞). The graph of this function is shown to the right. In SAS, you can use the QUAD subroutine in SAS IML software to perform numerical integration. Some numerical integrators have difficulty computing
