Accurate SVDs of polynomial Vandermonde matrices involving orthonormal polynomials

Accurate SVDs of Structured Matrices

We present new O(n) algorithms to compute very accurate SVDs of Cauchy matrices, Vandermonde matrices, and related \unit-displacement-rank" matrices. These algorithms compute all the singular values with guaranteed relative accuracy, independent of their dynamic range. In contrast, previous O(n) algorithms can potentially lose all relative accuracy in the tiniest singular values. LAPACK Working...

Accurate computations with Said-Ball-Vandermonde matrices

A generalization of the Vandermonde matrices which arise when the power basis is replaced by the Said-Ball basis is considered. When the nodes are inside the interval (0, 1), then those matrices are strictly totally positive. An algorithm for computing the bidiagonal decomposition of those Said-Ball-Vandermonde matrices is presented, which allows to use known algorithms for totally positive mat...

Accurate Eigenvalues and SVDs of Totally Nonnegative Matrices

Accurate SVDs of weakly diagonally dominant M-matrices

We present a new O(n 3) algorithm which computes the SVD of a weakly diagonally dominant M-matrix to high relative accuracy. The algorithm takes as an input the offdiagonal entries of the matrix and its row sums.

Polynomials and Vandermonde Matrices over the Field of Quaternions

It is known that the space of real valued, continuous functions C(B) over a multidimensional compact domain B ⊂ R , k ≥ 2 does not admit Haar spaces, which means that interpolation problems in finite dimensional subspaces V of C(B) may not have a solutions in C(B). The corresponding standard short and elegant proof does not apply to complex valued functions over B ⊂ C. Nevertheless, in this sit...