ill-conditioned matrix

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14:54 Mar 22, 2011
English to Croatian translations [PRO]
Tech/Engineering - Mathematics & Statistics
Additional field(s): Physics
English term or phrase: ill-conditioned matrix
Definition from Washington State University - Math:
We call a square matrix A ill-conditioned if it is invertible but can become non-invertible (singular) if some of its entries are changed ever so slightly. The condition number of A is a measure of how ill-conditioned A is and can be found using A and A-1. The bigger the condition number is the more ill-conditioned A is. Well-conditioned matrices have condition numbers close to 1.

Example sentence(s):
  • Ill-conditioned matrices and matrix condition numbers are discussed and an efficient and reliable indicator of ill-conditioned matrices is suggested WILEY online Library
  • Conditioning (9.11.) [TB, Lect. 12] examples for cancellation and an ill-conditioned matrix. Technische Universität München, WS 201
  • The condition number is a measure of stability or sensitivity of a matrix (or the linear system it represents) to numerical operations. In other words, we may not be able to trust the results of computations on an ill-conditioned matrix. Planet Math.org
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Summary of translations provided
5loše uvjetovana matrica
Nevenchi


  

Translations offered


16 days   confidence: Answerer confidence 5/5
loše uvjetovana matrica


Definition from own experience or research:
Loše uvjetovana matrica je matrica s (vrlo) velikim brojem uvjetovanosti.

Example sentence(s):
  • Ako je matrica loše uvjetovana (cond (A) je puno veći od 1), već male pogreške u elementima matrice A ili vektoru b proizvest će velike pogreške u vektoru rješenja x. - www.mathos.hr  
  • Osim toga, ako je matrica A loše uvjetovana, kod tog sustava možemo lakše koristiti iterativno profinjavanje rješenja. - numerička matematika  

Explanation:
Broj uvjetovanosti, koji karakterizira uvjetovanost matrice kao dobru ili lošu, računa se pomoću normi matrice i njoj inverzne matrice. Inverz se može odrediti samo za regularnu matricu. Dobro uvjetovana matrica (regularna) ima mali broj uvjetovanosti (blizu 1), dok singularna matrica ima beskonačan broj uvjetovanosti.

cond (A) = ||A|| ||A^(-1)||
Nevenchi
Local time: 10:13
Native speaker of: Native in CroatianCroatian
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