Several computational and structural properties of Bezoutian matrices expressed with respect to the Bernstein polynomial basis are shown. The exploitation of such properties allows the design of fastâ€¦ (More)

An algorithm based on the Ehrlichâ€“Aberth iteration is presented for the computation of the zeros of p(Î») = det(Tâˆ’Î»I), where T is a real irreducible nonsymmetric tridiagonal matrix. The algorithmâ€¦ (More)

Let Hn âŠ‚ CnÃ—n be the class of n Ã— n Hessenberg matrices A which are rank-one modifications of a unitary matrix, that is, A = H + uwH , where H is unitary and u,w âˆˆ Cn. The class Hn includes threeâ€¦ (More)

We show that the shifted QR iteration applied to a companion matrix F maintains the weakly semiseparable structure of F . More precisely, if Ai âˆ’ Î±iI = QiRi, Ai+1 := RiQi + Î±iI, i = 0, 1, . . .,â€¦ (More)

An implicit version of the shifted QR eigenvalue algorithm given in [D. A. Bini, Y. Eidelman, I. Gohberg, L. Gemignani, SIAM J. Matrix Anal. Appl. 29 (2007), no. 2, 566â€“585] is presented forâ€¦ (More)

Many superfast methods that for the inversion of an IZ X n Toeplitz matrix require O(n log*n) arithmetic operations and linear storage have been proposed (see, e.g., [2,6,7,9]). Since Hankel matricesâ€¦ (More)

We introduce a class Cn of n Ã— n structured matrices which includes three well-known classes of generalized companion matrices: tridiagonal plus rank-one matrices (comrade matrices), diagonal plusâ€¦ (More)

VANDERMONDE-LIKE MATRICES LUCA GEMIGNANI Abstract. This paper is concerned with the solution of linear systems with coe cient matrices which are Vandermonde-like matrices modi ed by adding low-rankâ€¦ (More)