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Unformatted text preview: 2.29: Numerical Fluid Mechanics Problem Set 3 MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MASSACHUSETTS 02139 2.29 NUMERICAL FLUID MECHANICS SPRING 2007 Problem Set 3 Totally 120 points Posted 04/03/07, due Thursday 4 p.m. 04/19/07, Focused on Lecture 8 to 17 Problem 3.1 (15 points): Consider the following system of equations: Ax = b , A = 1 2 ! 1 2 8 ! 1 4 " # $ $ $ % & , b = 8 4 " # $ $ $ % & a) Cholesky factorize A (Note that A is positive definite). b) Find an LU factorization form for A. c) Use LU factorization of A to find x. d) Compute the x ! = 1.5 by two iterations of successive over-relaxation scheme. Use relaxation parameter and initial guess of zero. e) Compute the solution by 4 iterations of conjugate gradient method. Problem 3.2 (10 points): Polynomial Interpolation Consider the below (x,y) pairs: x = ! 2 1 2 " # $ $ $ $ % & , y = f ( x ) = 2 1 ! 2 " # $ $ $ $ % & a) Find the Lagrange polynomial for above points. Find the Lagrange polynomial for above points....
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.29 taught by Professor Henrikschmidt during the Spring '07 term at MIT.
- Spring '07
- Mechanical Engineering