Questions tagged [condition-number]

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.

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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
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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) =…
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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…
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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…
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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
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