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program2 - Program 2 Foundations of Computational Math 1...

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Program 2 Foundations of Computational Math 1 Fall 2009 Due date: via email by 11:59PM on Wednesday, 10 November 1 General Task Your task is to implement and test the capabilities of solving a particular family of linear sytems via the Jacobi, Gauss Seidel, and Symmetric Gauss Seidel methods. Your code must be able to run in single and double precision. It should also efficiently store the matrix and perform the required matrix-vector products and linear system solves Mz k = r k . You will be asked to run particular scenarios and analyze the results. 2 Submission of Results Expected results comprise: 1. A document describing the tests used, the results generated, and answers to the ques- tions posed below. 2. The source code, makefiles, and instructions on how to compile and execute your code including the math department’s machine used if applicable. 3. Code documentation should be included in each routine. These results should be emailed to [email protected] by 11:59PM on the due date above. You may be asked to demonstrate your code if your document does not completely convince me that you tested your code sufficiently. 3 Code Details 3.1 Matrix Family You will write code to solve Ax = b where A is an n × n matrix with the form T α = α - 1 0 . . . . . . . . . 0 - 1 α - 1 0 . . . . . . 0 0 - 1 α - 1 0 . . . 0 . . . . . . . . . . . . . . . 0 . . . 0 - 1 α - 1 0 0 . . . . . . 0 - 1 α - 1 0 . . . . . . . . . 0 - 1 α 1
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3.2 Requirements of Code Your code must use O (1) storage for the matrix A for any size n . The computation of the matrix vector product Av w must be done efficiently in O ( n ) computations using the efficient storage scheme. The solution of systems Mz k = r k or any others required in each iteration must be done efficiently in O ( n ) computations using the efficient storage scheme.
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  • Spring '11
  • Gallivan
  • Articles with example pseudocode, Gauss–Seidel method, Jacobi method, Gauss Seidel, Symmetric Gauss Seidel

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