MAD4401Quiz4 - MAD 4401 Quiz 4 James Keesling 1 Linear...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAD 4401 Quiz 4 James Keesling 1 Linear Ordinary Differential Equations Problem 1.1. Solve the following systems of ordinary differential equations using matrix methods. d2 x = 4x dt2 d2 x dx −3· + 2x = 0 dt2 dt 2 Matrix Norms and Condition Number Problem 2.1. Compute the operator norm for the following matrix. Do this for the maximum norm and for the sum norm. 1 2 0 −1 7 0 −1 100 0 −32 0 17 0 0 −320 67 0 32 10 3 −7 0 5 −2 1 −13 −7 2 1 −25 2 5 −720 0 51 3 Problem 2.2. Determine the condition number for the matrix in Problem 2.1 for both the maximum norm and for the sum norm. Problem 2.3. Compute the condition number for the Hilbert matrix of size n × n for n = 5, 10, and 15. Problem 2.4. Compute the inverse of the Hilbert matrix for n = 4. Do this exactly. Problem 2.5. Compute the inverse of the Hilbert matrix for n = 8 exactly. Convert this Hilbert matrix to floating point entries and compute the inverse. Compare these two answers. What does the condition number for this matrix say about this comparison? 1 ...
View Full Document

Ask a homework question - tutors are online