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- Beatrice Meini
- Math. Comput.
- 2002

We propose a new quadratically convergent algorithm, having a low computational cost per step and good numerical stability properties, which allows the simultaneous approximation of the extreme solutions of the matrix equations X + A * X −1 A = Q and X − A * X −1 A = Q. The algorithm is based on the cyclic reduction method.

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

- Dario Bini, Bruno Iannazzo, Beatrice Meini
- Fundamentals of algorithms
- 2012

This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars. It is the first book in which nonsymmetric algebraic Riccati equations are treated in a clear and systematic way.… (More)

- Chun-Hua Guo, Bruno Iannazzo, Beatrice Meini
- SIAM J. Matrix Analysis Applications
- 2007

Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible M-matrix M are considered. The emphasis is on the case where M is an irreducible singular M-matrix, which arises in the study of Markov models. The doubling algorithm is considered for finding the minimal nonnegative solution, the one of practical interest.… (More)

- Dario Bini, Nicholas J. Higham, Beatrice Meini
- Numerical Algorithms
- 2004

New theoretical results are presented about the principal matrix pth root. In particular, we show that the pth root is related to the matrix sign function and to the Wiener–Hopf factorization, and that it can be expressed as an integral over the unit circle. These results are used in the design and analysis of several new algorithms for the numerical… (More)

- Dario Bini, Beatrice Meini, Federico Poloni
- Math. Comput.
- 2010

We propose a new matrix geometric mean satisfying the ten properties given by Ando, Li and Mathias [Linear Alg. Appl. 2004]. This mean is the limit of a sequence which converges superlinearly with convergence of order 3 whereas the mean introduced by Ando, Li and Mathias is the limit of a sequence having order of convergence 1. This makes this new mean very… (More)

We develop algorithms for the computation of the distribution of the total reward accrued during [0, t) in a finite continuous-parameter Markov chain. During sojourns , the reward grows linearly at a rate depending on the state visited. At transitions, there can be instantaneous rewards whose values depend on the states involved in the transition. For… (More)

- C. He, Beatrice Meini, Noah H. Rhee
- SIAM J. Matrix Analysis Applications
- 2002

A shifted cyclic reduction algorithm has been proposed by He, Meini, and Rhee [SIAM J. Matrix Anal. Appl., 23 (2001), pp. 673–691] for finding the stochastic matrix G associated with discrete-time quasi-birth-death (QBD) processes. We point out that the algorithm has quadratic convergence even for null recurrent QBDs. We also note that the approximations… (More)

- Richard A. Brualdi, Volker Mehrmann, +8 authors Eugene Tyrtyshnikov
- 1992

DESCRIPTION. Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other… (More)

- Beatrice Meini
- NAA
- 2000