This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 12 LU Decomposition In many applications where linear systems appear, one needs to solve A x = b for many different vectors b . For instance, a structure must be tested under several different loads, not just one. As in the example of a truss (9.2), the loading in such a problem is usually represented by the vector b . Gaussian elimination with pivoting is the most efficient and accurate way to solve a linear system. Most of the work in this method is spent on the matrix A itself. If we need to solve several different systems with the same A , and A is big, then we would like to avoid repeating the steps of Gaussian elimination on A for every different b . This can be accomplished by the LU decomposition , which in effect records the steps of Gaussian elimination. LU decomposition The main idea of the LU decomposition is to record the steps used in Gaussian elimination on A in the places where the zero is produced. Consider the matrix: A = 1 2 3 2 5 12 2 10 . The first step of Gaussian elimination is to subtract 2 times the first row from the second row. In order to record what we have done, we will put the multiplier, 2, into the place it was used to make...
View
Full Document
 Fall '08
 Young,T
 Determinant, Vectors, Linear Systems, Triangular matrix

Click to edit the document details