In this paper, we first provide a re-parametrization of the class of quasi-h-Bernstein-Vandermonde matrix and the parameters are calculated with high relative accuracy. Then, we present new algo-rithms for computing all the eigenvalues of such matrix to high relative accuracy. Finally, numerical...
the vandermonde matrix and its inverse play the important role of mapping between coefficient space and value space. when a non-monomial basis \(\{\phi _i(z)\}\) is used, \((v)_{ij} =\phi _{j-1}(\gamma _i)\) . we denote by \(v_i\) the matrix of first i columns of v...
Quasi-Cauchy-Vandermonde matrixGeneralized sign regular matricesHigh relative accuracyIn this paper, we consider the eigenvalue problem for the class of quasi-Cauchy-Vandermonde (qCV) matrices belonging to the class of generalized sign regular matrices with signature (1,…,1,1). We present the ...
Quasi-rational Said–Ball–Vandermonde matrixEigenvalueRelatively robust representationsHigh relative accuracyThis paper focuses on computing the eigenvalues of the generalized collocation matrix of the rational Said–Ball basis, also called as the quasi-rational Said–Ball–Vandermonde (q-RSBV) matrix, ...
The behavior of the minimum eigenvalue is considered by studying the behavior of the maximum eigenvalue of the inverse matrix. In particular, we prove that the minimum eigenvalue λV, as well as a some numerical examinations of the size of the atom at 0 for the random Vandermonde eigen...
We obtain some results about the block eigenvalues of block compound matrices and additive block compound matrices. Assuming that a certain block Vandermonde matrix is nonsingular, we generalize known results for (scalar) compound and additive compound matrices.José Victória...
Eigenvalues of Euclidean random matrices - Bordenave - 2008 () Citation Context ...am matrix concern Gaussian matrices [52] or matrices with independent entries. Very few results are available in the literature on matrices whose structure is strongly related to the Vandermonde case =-=[53, 54]...
the problem is reduced to a finite nonlinear eigenvalue problem of the kind WU(\\lambda){\\bf v}=0 WU(\\lambda){\\bf v}=0 , where W W is a constant matrix and U U depends on \\lambda \\lambda and can be given in terms of either a Vandermonde matrix or a companion matrix....
Cauchy, Vandermonde and Hankel matrices. The distinctive feature of accurate algorithms is using the intrinsic parameters that define such matrices to obtain a non-orthogonal factorization, such as the \textsf{LDU} factorization, and then computing the singular values of the product of thus computed...