NX Nastran Numerical Methods User’s Guide Proprietary & Restricted Rights Notice © 2007 UGS Corp. All Rights Reserved. This software and related documentation are…

Slide 1Copyright © 2007 Pearson Addison-Wesley. All rights reserved. A. Levitin Introduction to the Design & Analysis of Algorithms, 2 nd ed., Ch. 1 Chapter 2 Fundamentals…

Slide 1 Slide 2 Introduction: LU Decomposition is very useful when we have large matrices n x n and if we use gauss-jordan or the other methods, we can get errors. Computers…

Slide 1 Free Powerpoint Templates Page 1 Free Powerpoint Templates Computational Methods Dr Houssem Bouchekara 7. Direct Methods for Solving Linear Systems Slide 2 Free Powerpoint…

Slide 1 LU method 1) factor (decompose) A into L and U 2) given b, determine d 3) using Ux=d and backsubstitution, solve for x Advantage: Once you have L and U, can use many…

Slide 1 QR Factorization –Direct Method to solve linear systems Problems that generate Singular matrices –Modified Gram-Schmidt Algorithm –QR Pivoting Matrix must be…

Slide 1 Thomas algorithm to solve tridiagonal matrices Slide 2 Basically sets up an LU decomposition three parts 1) decomposition 2) forward substitution 3) backward substitution…

Slide 1 Square n-by-n Matrix Slide 2 Solution of Simultaneous Linear Equations Slide 3 Gaussian Elimination Forward Elimination 2 u + v + w = 1 (1) 4 u + v = -2 (2) -2 u…

Slide 1 High Performance Computing: Concepts, Methods & Means HPC Libraries Hartmut Kaiser PhD Center for Computation & Technology Louisiana State University April…