Date: Wed, 05 Sep 2007 15:36:16
From: S Bond
Subject: Tips for Homework 2
2.18) Symbolically multiply a (2 by 2) lower triangular matrix, L, with a (2 by 2) upper triangular matrix U. Show that it is not possible for this product to yield A as a result. 2.35) The definition of positive definite is on page 84 of the textbook (section 2.5) and page 67 of the course notes. 3.3) Just set up the system, don't solve it. 2.6 Computer Problem) You may use the 'hilb' command in Matlab to create the matrix, H. Matlab will compute the infinity norm if you use norm(x,inf). To estimate the number of correct digits we can use the (negative) log (base 10) of the relative error. You may use Matlab's 'cond' command to get the condition number of the matrix. For plotting the cond(H) vs. n and digits, try using a log scale for cond(H). The semilogy and semilogx commands will allow you to plot only one axis with a log scale. 2.10 Computer Problem) You may use the backslash operator to solve the linear system: x = A \ b . Type 'help slash' in Matlab for details on the different uses of forward and backward slashes. If you get the order wrong, or use the wrong slash, you probably will not get what you expect. Matlab stores the value for machine epsilon as 'eps'. Create a "table of results" comparing the relative accuracy in each component with the error bound involving the condition number. Once again, you can use Matlab's 'cond' command to get the condition number.