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Condition number - Wikipedia
A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned. en.wikipedia.org
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[PDF] Ill-conditioned Matrices
The coefficient matrix is called ill-conditioned because a small change in the constant coefficients results in a large change in the solution. A condition ... emtiyaz.github.io
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What is the difference between ill-conditioned and ill-posed?
An ill-conditioned problem would be well-posed when the number is large and finite, and ill-posed when it's infinite. math.stackexchange.com
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ill-conditioned
ill-conditioned, a. (ˈɪlkənˈdɪʃənd) [f. ill condition + -ed2.] Having bad ‘conditions’ or qualities; of an evil disposition; in a bad condition or state. In Geometry, applied to a triangle which has very unequal angles, such as that by which a star's parallax is determined.1614 Raleigh Hist. World i... Oxford English Dictionary
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Ill-Conditioned System - an overview | ScienceDirect Topics
Ill-conditioned systems refer to linear systems where a small perturbation in the matrix or the right-hand side can lead to a large variation in the exact ... www.sciencedirect.com
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ILL-CONDITIONED Definition & Meaning - Merriam-Webster
The meaning of ILL-CONDITIONED is having a bad temper or mean disposition : surly, irritable. How to use ill-conditioned in a sentence. www.merriam-webster.com
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Well-posed problem
Even if a problem is well-posed, it may still be ill-conditioned, meaning that a small error in the initial data can result in much larger errors in the An ill-conditioned problem is indicated by a large condition number. wikipedia.org
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Ill-Conditioned & Condition Number - Statistics How To
A mathematical problem or series of equations is ill-conditioned if a small change in input leads to a large change in the output. www.statisticshowto.com
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9: Adequacy of Solutions - Mathematics LibreTexts
A system of equations is considered to be ill-conditioned if a small change in the coefficient matrix or a small change in the right hand side ... math.libretexts.org
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Conditioned Problem - an overview | ScienceDirect Topics
A problem (with respect to a given set of data) is called an ill-conditioned or badly conditioned problem if a small relative error in data can cause a large ... www.sciencedirect.com
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What is ill-conditioning for systems of linear equations? - Quora
The matrix is ill-conditioned. Now what is meant by the ill - conditioned system? Assume the equations below -. www.quora.com
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What is the best way to solve a ill-conditioned linear problem?
Ill-conditioning is sometimes an artificial result from taking a bad choice of basis (or bad choice of something else) that results in an ill- ... discourse.julialang.org
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Ill-conditioned matrices and their singular values For ill-conditioned matrices, must it be that the smallest singular value is arbitrarily close to $0$? I know that $K_2(A) = \frac{\sigma_{max}}{\sigma_{min}}$ where ...
Of course. Think of the matrix $A$ defined as $$ A = \mathrm{diag}(1, 2, \ldots, N), $$ where $\mathrm{diag}$ is the diagonal matrix. For any value $N$, the condition number of the matrix will be $K_2(A) = N$ and the smallest singular value $\sigma_{\min} = 1$. The matrix can also be small, for exam...
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Ill-conditioned matrix > **Possible Duplicate:** > Inverse matrices are close iff matrices are close Consider this problem: **$Ax = b$** I want to solve it/find x and the matrix A is ill-conditioned. Why is the ...
Because if one knows the coefficients of $A$ only up to a given precision, a small variation in them will cause a huge variation in the coefficients of $A^{-1}$, hence, presumably, in the solution $x=A^{-1}b$. Alternatively, even if $A^{-1}$ is known with an absolute precision, if one knows the coef...
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Geometric interpretation of an ill-conditioned matrix Given a non-singular matrix $A\in$ $\Bbb R^{n\times n}$ (invertible) with SVD decomposition $(U, \Sigma, V)$, how would you interpret geometrically $A$ being ill c...
The worse-conditioned the matrix, the "skinnier" the ellipsoid.
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