Posts Tagged ‘ Numerical Analysis ’

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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Optimizing a function that evaluates an integral

March 5, 2014
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Optimizing a function that evaluates an integral

SAS programmers use the SAS/IML language for many different tasks. One important task is computing an integral. Another is optimizing functions, such as maximizing a likelihood function to find parameters that best fit a set of data. Last week I saw an interesting problem that combines these two important tasks.
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Define functions with default parameter values in SAS/IML

February 10, 2014
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Define functions with default parameter values in SAS/IML

One of my favorite new features of SAS/IML 12.1 enables you to define functions that contain default values for parameters. This is extremely useful when you want to write a function that has optional arguments. Example: Centering a data vector It is simple to specify a SAS/IML module with a
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A simple way to find the root of a function of one variable

February 5, 2014
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A simple way to find the root of a function of one variable

Finding the root (or zero) of a function is an important computational task because it enables you to solve nonlinear equations. I have previously blogged about using Newton's method to find a root for a function of several variables. I have also blogged about how to use the bisection method
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