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- Dario Bini, Victor Y. Pan
- Progress in theoretical computer science
- 1994

- Dario Bini, Milvio Capovani, Francesco Romani, Grazia Lotti
- Inf. Process. Lett.
- 1979

- Dario Bini, Beatrice Meini
- SIAM J. Matrix Analysis Applications
- 1996

- Dario Bini
- Numerical Algorithms
- 1996

An algorithm for computing polynomial zeros, based on Aberth's method, is presented. The starting approximations are chosen by means of a suitable application of Rouché's theorem. More precisely, an integerq ≥ 1 and a set of annuliA i,i=1,...,q, in the complex plane, are determined together with the numberk i of zeros of the polynomial contained in each… (More)

- Dario Bini, Paola Boito
- ISSAC
- 2007

The relationship between univariate polynomial ∈-gcd and factorization of resultant matrices is investigated and several stable and effective algorithms for the computation of an ∈-gcd are proposed. The main result is the design of a practically stable algorithm whose arithmetic cost is quadratic in the degrees of the input polynomials. The… (More)

- Dario Bini
- SIAM J. Comput.
- 1984

- Dario Bini, Giuseppe Fiorentino
- Numerical Algorithms
- 2000

We present the design, analysis, and implementation of an algorithm for the computation of any number of digits of the roots of a polynomial with complex coefficients. The real and the imaginary parts of the coefficients may be integer, rational, or floating point numbers represented with an arbitrary number of digits. The algorithm has been designed to… (More)

- Dario Bini, Yuli Eidelman, Luca Gemignani, Israel Gohberg
- SIAM J. Matrix Analysis Applications
- 2007

Let Hn ⊂ Cn×n be the class of n × 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 ∈ Cn. The class Hn includes three well-known subclasses: unitary Hessenberg matrices, companion (Frobenius) matrices, and fellow matrices. The paper presents some novel fast adaptations of the… (More)

- Dario Bini, Beatrice Meini, S. Steffé, Benny Van Houdt
- SMCtools '06
- 2006

We analyze the problem of the numerical solution of structured Markov chains encountered in queuing models: we describe the main computational problems and present the most advanced algorithms currently available for their solutions.

We describe the implementation and the use of the package MPSolve (Multiprecision Polynomial Solver) for the approximation of the roots of a univariate polynomial p(x) = ∑n i=0 aix . The package relies on an algorithm, based on simultaneous approximation techniques, that generates a sequence A1 ⊃ A2 ⊃ . . . ⊃ Ak of nested sets containing the root… (More)