João Batista da Paz Carvalho

A new block algorithm for full-rank solution of the Sylvester-observer equation

A new block algorithm for computing a full rank solution of the Sylvester-observer equation arising in state estimation is proposed. The major computational kernels of this algorithm are: 1) solutions of standard Sylvester equations, in each case of which one of the matrices is of much smaller order than that of the system matrix and (furthermore, this small matrix can be chosen arbitrarily), and 2) orthogonal reduction of small order matrices. There are numerically stable algorithms for performing these tasks including the Krylov-subspace methods for solving large and sparse Sylvester equations. The proposed algorithm is also rich in Level 3 Basic Linear Algebra Subroutine (BLAS-3) computations and is thus suitable for high performance computing. Furthermore, the results on numerical experiments on some benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem.

Laplacian energy of diameter 3 trees

Abstract Let T n be the set of all trees of diameter 3 and n vertices. We show that the Laplacian energy of any tree in T n is strictly between the Laplacian energy of the path P n and the star S n , partially proving the conjecture that this holds for any tree. We also give a total order by the Laplacian energy in T n . Moreover, we show that this order depends only on the algebraic connectivity of the tree: the Laplacian energy increases as the algebraic connectivity decreases in T n .

An algorithm for generalized Sylvester-observer equation in state estimation of descriptor systems

An algorithm for solving the generalized Sylvester-observer equation arising in state estimation of descriptor systems is proposed. The algorithm is structure preserving and rich in BLAS-3 computations and thus suitable for high performance computing. The algorithm is a generalization of the one recently proposed by Datta and Sarkissian in state-estimation of standard first-order state space systems. The algorithm can be used in state estimation of matrix second-order control systems, and an algorithm for this purpose is given.

A block algorithm for the Sylvester-observer equation arising in state-estimation

We propose an algorithm for solving the Sylvester-observer equation arising in the construction of the Luenberger observer. The algorithm is a block-generalization of P. Van Doorens (1981) scalar algorithm. It is more efficient than Van Doorens algorithm and the recent block algorithm by B.N. Datta and D. Sarkissian (2000). Furthermore, the algorithm is well-suited for implementation on some of todays powerful high performance computers using the high-quality software package LAPACK.

A new algorithm for generalized Sylvester‐observer equation and its application to state and velocity estimations in vibrating systems

We propose a new algorithm for block-wise solution of the generalized Sylvester-observer equation XA−FXE = GC, where the matrices A, E, and C are given, the matrices X, F, and G need to be computed, and matrix E may be singular. The algorithm is based on an orthogonal decomposition of the triplet (A, E, C) into the observer-Hessenberg-triangular form. It is a natural generalization of the widely known observer-Hessenberg algorithm for the Sylvester-observer equation: XA−FX = GC, which arises in state estimation of a standard first-order state-space control system. An application of the proposed algorithm is made to state and velocity estimations of second-order control systems modeling a wide variety of vibrating structures. For dense un-structured data, the proposed algorithm is more efficient than the recently proposed SVD-based algorithm of the authors. Copyright

The composite character of the twenty-second Fermat number

AbstractA machine computation has been carried out to show that the twenty-second Fermat numberF22=

A new block algorithm for solving the Sylvester-observer equation

2^{2^{22} }

Parametric effects in nanobeams and AFM

+1 is composite.