the condition number κ(A) measures: sensitivity of Ax=b to perturbations

Condition number κ(A) measures sensitivity of Ax=b to perturbations

The condition number κ(A) quantifies how small changes in the input can lead to large changes in the output when solving Ax=b. It is crucial in numerical analysis for assessing the stability and reliability of solutions to equations.

Example

If A is a matrix representing a linear system and κ(A) is large, then small errors in the input vector b can cause significant errors in the solution vector x.

Remember this

Understanding κ(A) helps in choosing appropriate numerical methods and ensuring accurate solutions to linear systems.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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