The condition number of a matrix is the ratio of the largest to the smallest singular value in the singular value decomposition of a matrix.
Questions tagged [condition-number]
284 questions
3
votes
1 answer
Relative condition number, Ill conditioned, Well conditioned
I'm currently learning about relative condition number (K), and how they are considered as well conditioned or ill conditioned.
From my understanding, a large K value represents ill-conditioned, while a small K value represents…
Kevin
- 57
2
votes
1 answer
Matrix and its condition number
This example is given in Higham [2002], and is provided without explanation. I am not sure how the condition number of the matrix is just 5. How can you directly calculate the condition number of a matrix with epsilon? I know that cond(A) =…
lnormnorm
- 23
1
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0 answers
Condition number - eigenvalues
I have the following matrix
\begin{bmatrix}
15.52 & 0.00 & -14.52 \\
-11.05 & 1.00 & 11.05 \\
-0.01 & 0.00 & 0.01
\end{bmatrix}
I am supposed to calculate the condition number as the ratio between its maximum and minimum eigenvalue. My result…
Felipe Ca
- 11
1
vote
1 answer
Finding the relative condition number given a function.
I'm teaching myself how to find the relative condition numbers and I am struggling with connecting it to something basic like scalar multiplication. For example, the first problem of my text book seems simple enough, $f(x_1,x_2) = X_1 * X_2$ with…
Gabriel Fair
- 113
1
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0 answers
At which point is a condition # considered ill-conditioned?
At which point is a condition # considered ill-conditioned?
In my opinion, a condition # of $10^{10}$ corresponds to ill-conditioning obviously.
But what about a condition # of say, $2000$? $200$? $20$?
24n8
- 1,455