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Title: Scientific Computation II
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Abstract: Columbia University Department of Computer Science Fall 1999 Course: CSW3251 (Scientific Computation II) Instructor: Jerry B. Altzman ( TAs: Tracy A. Hammond ( Simon Shamoun ( WWW: Office hours: TBA Prerequisites: Scientific Computation I, Calculus Syllabus: This course consists of both a multivariate version of Sci. Comp I and an introduction to linear algebra. We will attempt to develop a geometric intuition for linear algebra throughout. * Recap of numerical arithmetic * Recap of analysis numerical algorithms * Measures of error * Stability * Complexity * Introduction to matrices and vector spaces * Notation and nomenclature * Norms * Spaces * Determinants * Numerical solutions to linear systems * Gaussian elimination * Standard decompositions (LU, Cholesky) * Least Squares problems and the SVD * Eigenvalue problems * Power method(s) * QR methods * Iterative methods * Linear systems (Gauss-Seidel, Jacobi, SOR) * Eigenvalue problems* * Linear programming (the simplex method) * Multivariate not-so-linear problems * Rootfinding * Optimization* * Integration* * Interpolation* Textbook: Required: Demmel, James L. Applied Numerical Linear Algebra Goldberg, D. What Every Computer Scientist Should Know About Floating-Point Arithmetic, in ACM Computing Surveys, also available in a few other places. Recommended: Golub, G. & C. Van Loan, Matrix Computations Press, et al., Numerical Recipes Overview: We will try to stick to the book for the numerical work. However, the book presupposes knowledge of linear algebra, so I will supplement that with my lectures. So, yes, class attendance is important if you don�t already know linear algebra. I�ll also be drawing significantly from sources outside the text. Your grade will be determined in the following way: Homework 15% Midterm 35% Final 50% Homework will be assigned about once every three lectures, and are due two lectures after their assignment. Homework will be accepted up to one week late but with a 50% penalty. You may collaborate on homework but each student must hand in his or her own work (i.e. no group submissions). The homework will be split between programming (implementation) and theory (pencil-and-paper). You may use any programming language that suits your fancy. However, MATLAB is available for student use and you may find that the most useful tool. (Some homework might require the use of MATLAB.)
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