Linear Algebra and Its Applications · Problem 7.4.5

Linear Programming and Game Theory — Gilbert Strang

Mathematics · gershgorin-circle-theorem-jacobi-convergence

Problem

Write the Jacobi matrix

J

for the diagonally dominant

A

of Problem 4, and find the three Gershgorin circles for

J

. Show that all the radii satisfy

r_i < 1

, and that the Jacobi iteration converges.