Vandermonde matrixColliding nodesCondition numberFrequency analysisSuper resolutionWe prove upper and lower bounds for the spectral condition number of rectangular Vandermonde matrices with nodes on the complex unit circle. The nodes are "off the grid," pairs of nodes......
The condition number of real Vandermonde, Krylov and positive definite Hankel matrices We show that the Euclidean condition number of any positive definite Hankel matrix of order nges3 may be bounded from below by gamma n-1/(16n) with gamma=e... B Beckermann - 《Numerische Mathematik》 被引...
Asymptotically Optimal Lower Bounds for the Condition Number of a Real Vandermonde Matrix Lower bounds on the condition number min kappa p(U) of a real Vandermonde matrix V are established in terms of the dimension n or n and the largest absolut... Li,Ren‐Cang - 《Siam Journal on Matrix...
matrices (ASM), in which the weight of each such matrix is equal to s N − , where N − is the 4 PAVEL BLEHER AND KARL LIECHTY number of (−1)’s in the matrix and s = 1 x 2 . The exact solution for a finite n is known for 1-, ...
Al-Dosary, Complex exponential Vandermonde determinant with application to discrete boundary value problem, Proceedings of the 7th International Conference on Difference Equations and Applications, Field Institute Communications, to appear. [3] R. Abu-Saris and H. Yousef, Existence theorems for ...
Vandermonde matrixColliding nodesCondition numberFrequency analysisSuper resolutionWe prove upper and lower bounds for the spectral condition number of rectangular Vandermonde matrices with nodes on the complex unit circle. The nodes are "off the grid," pairs of nodes nearly collide, and the studied ...
Condition Number of a Vandermonde Matrixdoi:10.1137/1038048Bradley K. AlpertSiam Review
We derive lower bounds for the ∞-condition number of the n×n -Vandermonde matrix V n (x) in the cases where the node vector x T =[x 1 , x 2 ,...,x n ] has positive elements or real elements located symmetrically with respect to the origin. The bounds obtained grow ...
The condition of Vandermonde-like matrices involving orthogonal polynomials - ScienceDirectThe condition number (relative to the Frobenius norm) of the n × n matrix P n = [ p i1( x j)] i, j = 1 n is investigated, where p r(·) = p r(·; dλ) are orthogonal polynomials with ...
Asymptotically optimal lower bounds for the condition number of a real Vandermonde matrix - Li - 2006 () Citation Context ...mputed (estimated). If �Rk+1�F can be estimated, too, bounds on κ 1/2(Vk+1,n) can be obtained. Indeed for pj = Tj, if τ is real and τ = 0 ...