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Questions tagged [condition-number]

For questions about calculating or interpreting condition numbers. Most commonly refers to the condition number of a matrix, but can be applied generally to analyzing the error in a function based on error in the input.

A condition number relates the error/deviation in some function/transformation to the error/deviation in its inputs.

A problem with low condition number means low sensitivity to small changes in input values, making the problem "well-conditioned". A problem with a large condition number has high sensitivity to small changes in input values, making the problem "ill-conditioned".

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Condition number of (A + cI) matrix

For given matrix $A \in R^{n\times n}$, identity matrix $I$ and constant $c > 0$ is this possible to express $cond(A + cI)$ knowing $cond(A)$ and $c$?
Alexander
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Is there a general threshhold for which a large condition number becomes "problematic?"

I think the answer is probably no in the linear algebra community, but I'd say anything above $10^8$ and you're starting to lose too much precision, making the situation problematic. In some statistics settings, where they use OLS, I've seen it…
David
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Whether should we consider the condition number of the preconditioned matrix when choosing a preconditioner?

when we solve a large sparse linear system Ax=b, using preconditioned Krylov subspace methods,e.g., gmres, should we need to reduce the condition number of the coefficient matrix? In my opinion, we just need to consider how to cluster the…
Happy
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Missing something fundamental about condition number estimation

In Higham's Accuracy and Stability of Numerical Algorithms, Chapter 15, algorithm 15.3 and 15.4: The topic is ostensibly condition number estimation, but these algorithms show how to compute $\gamma$ such that $\gamma < \left\|A\right\|_{1}$. But if…
user14717
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