Norms of inverses and condition numbers for matrices associated with scattered data

Condition Numbers of Matrices

denote its Euclidean operator norm (often called the 2-norm). If  is nonsingular, then its condition number () is defined by () = kk°°−1°° = 1() () where 1 ≥ 1 ≥    ≥  ≥ 0 are the singular values of . The s constitute lengths of the semi-axes of the hyperellipsoid  = { : kk = 1} in -dimensional space; thus  measures elongation of  at its extreme [1]. The role that  ...

Condition numbers of random matrices

A bound for condition numbers of matrices

Inversion error, condition number, and approximate inverses of uncertain matrices

The classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix. First, it assumes that the perturbation is infinitesimally small. Second, it does not take into account the perturbation structure (e.g., Vandermonde). Similarly, the classical notion of the inverse of a matrix neglects the possibility of large, structured perturbations. We d...

Norms of Circulant and Semicirculant Matrices with Horadam’s Numbers

In this paper, we obtain the spectral norm and eigenvalues of circulant matrices with Horadam’s numbers. Furthermore, we define the semicirculant matrix with these numbers and give the Euclidean norm of this matrix. 2000 Mathematics Subject Classification: 11B39; 15A36; 15A60; 15A18.