2
$\begingroup$

Suppose that I have a linear system $Ax=b$ such that $A$ is ill-conditioned. Can I say that it is dangerous to find a solution with Gaussian Elimination for this system, or does there exist some class of pivoting that allows me to find a good solution?

Does the Vandermonde Matrix have something special to do with this issue?

$\endgroup$

1 Answer 1

5
$\begingroup$

Ill conditioning is a property of the system of equations rather than the algorithm used to solve the system of equations. Using a bad algorithm can certainly make the situation worse, but you're already in trouble when you try to solve an ill-conditioned system of equations with A coefficients or right-hand side b with even tiny errors even if you use exact rational arithmetic. Similarly, you'll be in trouble if you use floating-point arithmetic with limited precision compared to the condition number.

Vandermonde matrices are typically extremely badly conditioned, so they are often used as examples of ill-conditioning.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.