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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2003 • Question 9

Question

Math 6610 • Analysis of Numerical Methods I Fall 2003 • Question 9

Ill Conditioning Define the condition number of a square matrix \(A\) and its significance for the solution of the linear system \[ Ax=b. \tag {5} \] Can you define a similar number that describes the conditioning of the eigenvalue problem \[ Ax=\lambda x? \tag {6} \]

Raw LaTeX

{Ill Conditioning}
Define the condition number of a square matrix \(A\) and its significance for the
solution of the linear system
\[
  Ax=b. \tag{5}
\]
Can you define a similar number that describes the conditioning of the eigenvalue
problem
\[
  Ax=\lambda x? \tag{6}
\]

Topic Tags

Conditioning, Sensitivity, and Perturbation Bounds Eigenvalues, Spectral Radius, and Gershgorin Theorem Iterative Methods for Linear Systems Linear Programming and Optimization