1 / 5

Understanding LU Factorization in Numerical Analysis

This introduction to LU Factorization explores its role as a matrix representation of Gaussian elimination. It covers essential concepts such as lower triangular matrices, row operations, and the principles behind LU factorization for systems of equations. The text includes propositions illustrating the mechanics of the factorization process, such as the representation of row operations by triangular matrices and the operation count necessary for solving n equations with n variables. This foundational knowledge is vital for students in mathematics and computer science.

eagan-wolf
Download Presentation

Understanding LU Factorization in Numerical Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Numerical Analysis I LU Factorization MATH/CMPSC 455

  2. LU Factorization LU-factorization is a matrix representation of Gaussian elimination

  3. Example: Example:

  4. Proposition: Let denote the lower triangular matrix whose only nonzero entries are 1’s on the main diagonal and –c in (i,j) position. The it represents the row operation “subtracting c times row j from row i.” Proposition: Proposition:

  5. Operation Count The LU factorization for a system of n equations in n variables can be completed by operations

More Related