Posts Tagged ‘ Numerical Analysis ’

Halley’s method for finding roots

August 24, 2016
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Halley’s method for finding roots

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

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All I really need to know about Newton’s method I learned in primary school

May 18, 2016
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All I really need to know about Newton’s method I learned in primary school

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

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Trap and cap: Avoid division-by-zero and domain errors when evaluating functions

November 4, 2015
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Trap and cap: Avoid division-by-zero and domain errors when evaluating functions

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

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The sensitivity of Newton’s method to an initial guess

June 24, 2015
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The sensitivity of Newton’s method to an initial guess

In my article about finding an initial guess for root-finding algorithms, I stated that Newton's root-finding method "might not converge or might converge to a root that is far away from the root that you wanted to find." A reader wanted more information about that statement. I have previously shown

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Finding roots: Automating the search for an initial guess

June 22, 2015
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Finding roots: Automating the search for an initial guess

A SAS programmer asked an interesting question on a SAS Support Community. The programmer had a nonlinear function with 12 parameters. He also had file that contained 4,000 lines, where each line contained values for the 12 parameters. In other words, the file specified 4,000 different functions. The programmer wanted

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Compute the rank of a matrix in SAS

April 8, 2015
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Compute the rank of a matrix in SAS

A common question from statistical programmers is how to compute the rank of a matrix in SAS. Recall that the rank of a matrix is defined as the number of linearly independent columns in the matrix. (Equivalently, the number of linearly independent rows.) This article describes how to compute the

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Create a custom PDF and CDF in SAS

March 6, 2015
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Create a custom PDF and CDF in SAS

In my previous post, I showed how to approximate a cumulative density function (CDF) by evaluating only the probability density function. The technique uses the trapezoidal rule of integration to approximate the CDF from the PDF. For common probability distributions, you can use the CDF function in Base SAS to

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Optimizing a function of an integral

March 12, 2014
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Optimizing a function of an integral

This post was kindly contributed by The DO Loop - go there to comment and to read the full post. Last week I showed how to find parameters that maximize the integral of a certain probability density function (PDF). Because the function was a PDF, I could evaluate the integral by calling the CDF...
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