Math. 655-01, Fall, 2001 Assignments
This list is updated as the assignments are made. Note that the
primary work for the course will be the projects. These assignments are
primarily for drill to clarify concepts and techniques presented in the
page for the course;
R. Baker Kearfott
Show that the componentwise interval extension of a Jacobi matrix F'(x)
over an interval vector x is a Lipschitz matrix.
Show that, if A (possibly an interval Jacobi matrix and possibly
an interval slope matrix) is used in the interval Gauss-Seidel method with
initial interval vector x and base point x^,
then the image under the interval Gauss-Seidel method contains all solutions
to A(x - x^)= - F(x^).
Hint: This can be shown by examining the derivation of the interval
Gauss-Seidel method from the mean value theorem. Consult me if you
have any questions about this.