scholarly journals Lower bounds for the condition number of a real confluent Vandermonde matrix

2006 ◽  
Vol 75 (256) ◽  
pp. 1987-1995 ◽  
Author(s):  
Ren-Cang Li
Keyword(s):  
Lower Bounds ◽  
Condition Number ◽  
Vandermonde Matrix

Lower bounds for the condition number of Vandermonde matrices

1987 ◽  
Vol 52 (3) ◽  
pp. 241-250 ◽  
Author(s):  
Walter Gautschi ◽  
Gabriele Inglese
Keyword(s):  
Lower Bounds ◽  
Condition Number ◽  
Vandermonde Matrices

scholarly journals On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes

2020 ◽  
Author(s):  
Stefan Kunis ◽  
Dominik Nagel
Keyword(s):  
Unit Circle ◽  
Lower Bounds ◽  
Condition Number ◽  
Growth Rates ◽  
Separation Distance ◽  
Upper And Lower Bounds ◽  
Spectral Condition ◽  
Sharp Constants ◽  
Vandermonde Matrices

Abstract We 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 grows linearly with the inverse separation distance. Such growth rates are known in greater generality if all nodes collide or for groups of colliding nodes. For pairs of nodes, we provide reasonable sharp constants that are independent of the number of nodes as long as non-colliding nodes are well-separated.

Condition Number of a Vandermonde Matrix

SIAM Review ◽  
1996 ◽  
Vol 38 (2) ◽  
pp. 314-314
Author(s):  
Bradley K. Alpert
Keyword(s):  
Condition Number ◽  
Vandermonde Matrix

scholarly journals On the condition number of the Vandermonde matrix of the nth cyclotomic polynomial

2020 ◽  
Vol 15 (1) ◽  
pp. 174-178
Author(s):  
Antonio J. Di Scala ◽  
Carlo Sanna ◽  
Edoardo Signorini
Keyword(s):  
Prime Number ◽  
Condition Number ◽  
Singular Values ◽  
Number Fields ◽  
Upper Bounds ◽  
Vandermonde Matrix ◽  
Cyclotomic Polynomial ◽  
Cyclotomic Number ◽  
Learning With Errors ◽  
Cyclotomic Number Fields

AbstractRecently, Blanco-Chacón proved the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for some families of cyclotomic number fields by giving some upper bounds for the condition number Cond(Vn) of the Vandermonde matrix Vn associated to the nth cyclotomic polynomial. We prove some results on the singular values of Vn and, in particular, we determine Cond(Vn) for n = 2kpℓ, where k, ℓ ≥ 0 are integers and p is an odd prime number.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base
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