Lecture15b - Solving Scalar Linear Systems Iterative...

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Solving Scalar Linear Systems Iterative approach Lecture 15 MA/CS 471 Fall 2003
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Some matlab scripts to construct various types of random circuit loop matrices are available at the class website:
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The Sparsity Pattern of a Loop Circuit Matrix for a Random Circuit (with 1000 closed loops) b
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gridcircuit.m An array of current loops with random resistors (resistors on circuit boundary not shown)
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b Matrix Due To Random Grid Circuit Note the large amount of structure in the loop circuit matrix
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The Limits of Factorization In the last class/lab we began to see that there are limits to the size of linear system solvable with matrix factorization based methods. The storage cost for the loop current matrix built on a Cartesian circuit stored as a sparse NxN matrix is ~ 5*N However, using LU (or Cholesky) and symmetric RCM the storage requirement is b*N which is typically at least an order of magnitude larger than the storage required for the loop matrix itself. Also – memory spent on storing the matrices is memory we could have used for extra cells…
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Alternative Approach We are going to pursue iterative methods which will satisfy the equation in an approximate way without an excessive amount of extra storage. There are a number of different classes of iterative methods, today we will discuss an example from the class of stationary methods. = Ax b http://www.netlib.org/linalg/html_templates/node9.html
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Jacobi Iteration Example system: Initial guess: Algorithm: i.e. for the I’th equation compute the I’th degree of freedom using the values computed from the previous iteration. 5
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This note was uploaded on 07/22/2011 for the course ME 3 taught by Professor Prof.ramachandran during the Spring '11 term at Indian Institute of Technology, Kharagpur.

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Lecture15b - Solving Scalar Linear Systems Iterative...

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