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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2019 • Question 4

Question

Math 6610 • Analysis of Numerical Methods I Fall 2019 • Question 4
**Jacobi Method** **a)** State the Jacobi method for the solution of the linear system \(Ax=b\), where \(A\in\mathbb{R}^{m\times m}\). **b)** Show that if \(A\) is a strictly diagonally dominant matrix by rows, the Jacobi method is convergent for any \(x^{(0)}\).

Raw LaTeX

{Jacobi Method}

\partitem{a} State the Jacobi method for the solution of the linear system
\(Ax=b\), where \(A\in\R^{m\times m}\).

\partitem{b} Show that if \(A\) is a strictly diagonally dominant matrix by rows,
the Jacobi method is convergent for any \(x^{(0)}\).

Topic Tags

Iterative Methods for Linear Systems Linear Programming and Optimization