Lecture24 - Algorithms in Systems Engineering IE170 Lecture...

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Unformatted text preview: Algorithms in Systems Engineering IE170 Lecture 24 Dr. Ted Ralphs IE170 Lecture 24 1 References for Today’s Lecture • Required reading – CLRS Chapter 28 IE170 Lecture 24 2 Continuous Mathematics • So far, all the algorithms we have studied have been for problems in discrete mathematics . • Discrete mathematics is the study of problems for which there are only a finite number of possible outcomes. • Algorithms for discrete problems typically only involve integer values. • Continuous mathematics is the study of problems for which the number of possible outcomes is infinite. • Algorithms for these problems typically involve real numbers. • The difficulty with such algorithms is that a computer is not capable of representing most real numbers exactly. • To represent a real number in a computer, the value must be rounded . • This can create serious problems for some algorithms. IE170 Lecture 24 3 Common Problems in Continuous Mathematics • Solving systems of equations • Finding the inverse of a matrix • Finding the eigenvalues or eigenvectors of a matrix • Least-squares problems • Solving systems of inequalities • Factoring a matrix IE170 Lecture 24 4 Floating-point Numbers • There are basically three schemes by which real numbers can be...
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Lecture24 - Algorithms in Systems Engineering IE170 Lecture...

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