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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2022 • Question 4

Question

Math 6610 • Analysis of Numerical Methods I Fall 2022 • Question 4

(Iterative Solvers).

  1. State Gauss-Seidel method for the solution of the linear system \(Ax = b\), where \(A \in \mathbb {R}^{m \times m}\).
  2. Show that if \(A\) is a strictly diagonally dominant matrix by rows, the Gauss-Seidel method is convergent for any \(x^{(0)}\).

Raw LaTeX

(Iterative Solvers).
\begin{enumerate}

\item
State Gauss-Seidel method for the solution of the linear system \(Ax = b\), where \(A \in \mathbb{R}^{m \times m}\).


\item
Show that if \(A\) is a strictly diagonally dominant matrix by rows, the Gauss-Seidel method
is convergent for any \(x^{(0)}\).

\end{enumerate}

Topic Tags

Iterative Methods for Linear Systems Jacobi and Gauss-Seidel Methods Linear Programming and Optimization