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ill-conditioned matrix

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14:55 Mar 22, 2011
English to Portuguese 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
5 +1matriz mal condicionada
Hugo Lopes (X)
5matriz mal condicionada
Gabriel Rosa


Discussion entries: 1





  

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7 hrs   confidence: Answerer confidence 5/5 peer agreement (net): +1
matriz mal condicionada


Definition from "Álgebra Linear" - Luis T. Magalhães:
As soluções de sistemas de equações podem ou não ser muito sensíveis a pequenas mudanças na matriz dos coeficientes. No primeiro caso, diz-se que a matriz dos coeficientes é "mal condicionada".

Example sentence(s):
  • Numa matriz mal condicionada as linhas ou colunas são aproximadamente linearmente dependentes e, por conseguinte, o seu determinante, se existir, é sempre muito próximo de zero. - Universidade de Coimbra  
  • Em problemas grandes em que a matriz de rigidez não seja muito mal condicionada, o método iterativo conduz a menores tempos de resolução. - Universidade do Porto  
  • Embora A - pI seja uma matriz mal condicionada a respeito da inversão – basta notar que se p é muito próximo do valor próprio então A - pI é quase singular (...) - Universidade do Minho  

Explanation:
O título completo do livro de onde foi tirada a definição é:

Álgebra linear como introdução à matemática aplicada
Luis T. Magalhães
Texto Editora
Hugo Lopes (X)
Portugal
Local time: 05:49
Native speaker of: Native in PortuguesePortuguese

Votes in favor of/against selecting this as the best translation of the term asked
Yes  Matheus Chaud
1700 days
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11 hrs   confidence: Answerer confidence 5/5
matriz mal condicionada


Definition from Resolução de Sistemas de Equações Li:
Matrizes com um número de condição elevado dizem-se mal condicionadas. Matrizes com um número de condição baixo dizem-se bem condicionadas.

Example sentence(s):
  • Esta matriz designa-se Matriz de Hilbert, e é extremamente mal condicionada. Com efeito, já para m = 3 obtemos Cond1 = 28375, e para m = 4 já atinge 943656, continuando a crescer fortemente! Temos, assim, problemas de condicionamento e consequentemente de instabilidade numérica, para este tipo de matrizes. - Método dos Mínimos Quadrados  
Gabriel Rosa
Portugal
Local time: 05:49
Native speaker of: Native in PortuguesePortuguese
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