21.15.2. Iterative Methods

Try these first

1. 1.

   What is an iterative method?

   Hint

   Think about solving equations step by step.

2. 2.

   Name one iterative method used in linear algebra.

   Hint

   It starts with 'G' or 'J'.

3. 3.

   What does the Gauss-Seidel method do?

   • Uses old values
   • Uses new values
   • Both

   Hint

   Think about how solutions are updated.

4. 4.

   True or False: The Jacobi method is faster than the Gauss-Seidel method.

   • True
   • False

   Hint

   Which method uses the latest values without delay?

5. 5.

   Consider a civil engineering project that requires analyzing the load distribution on a long bridge using an iterative method. Formulate a step-wise approach to use the Gauss-Seidel method effectively.

   Hint

   Remember to update the estimates as you progress through the equations.

6. 6.

   You are presented with a system of equations represented by a sparse matrix. Discuss the advantages of using an iterative method over a direct method in this case.

   Hint

   Focus on resource management and efficiency when working with sparse matrices.