Improving the condition number of estimated covariance matrices

Improving Bilingual Projections via Sparse Covariance Matrices

Mapping documents into an interlingual representation can help bridge the language barrier of cross-lingual corpora. Many existing approaches are based on word co-occurrences extracted from aligned training data, represented as a covariance matrix. In theory, such a covariance matrix should represent semantic equivalence, and should be highly sparse. Unfortunately, the presence of noise leads t...

Correction: Condition Number Estimation of Preconditioned Matrices

[This corrects the article DOI: 10.1371/journal.pone.0122331.].

Condition Number Estimation of Preconditioned Matrices

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained ...

On The Frobenius Condition Number of Positive Definite Matrices

The condition number of certain matrices and applications

This paper addresses the problem of estimating the eigenvalues and condition numbers of matrices of the form R = r(ti tj). We begin by mentioning some of the problems in which such matrices occur, and to which the results obtained in this paper may be applied. Examples of such problems include (i) approximation by sums of irregular translates (ii) the missing data problem and incomplete samplin...