9. Linear Systems II

Jacobi And Gauss-seidel Methods — Quiz

Test your understanding of jacobi and gauss-seidel methods with 5 practice questions.

Practice Questions

Question 1

In the Jacobi method for solving a linear system, what values are used to compute the new approximation at iteration $k+1$?

Question 2

What is the main feature of the Gauss-Seidel method that distinguishes it from Jacobi?

Question 3

For the system $x+y=2$ and $x-y=0$, with initial guess $x^{(0)}=0$ and $y^{(0)}=0$, what is the first Jacobi iterate $(x^{(1)},y^{(1)})$?

Question 4

For the same system and initial guess $x^{(0)}=0$ and $y^{(0)}=0$, what is the first Gauss-Seidel iterate $(x^{(1)},y^{(1)})$?

Question 5

Which matrix property is a sufficient condition for Jacobi and Gauss-Seidel to converge for many linear systems?