Encontrados 18 documentos, a visualizar página 1 de 2
Multistage iterative methods for symmetric positive definite matrices
Lu Xuejing; Liu Zhongyun; Zhang YulinIn this paper a multistage iterative method for solving the symmetric positive definite linear systems is established and the convergence of the method is proved. A numerical example is given to illustrate the effectiveness of our method. The method is especially suitable for parallel computation, and can be viewed as a extension of the classical iterative method or as a preconditioner for the conjugate gradien...
On computing complex square roots of real matrices
Liu Zhongyun; Zhang Yulin; Santos, Jorge M. F.; Ralha, RuiWe present an idea for computing complex square roots of matrices using only real arithmetic.
Shear behaviour of steel fibre reinforced self-consolidating concrete beams bas...
Ding, Yining; Zhang Fasheng; Torgal, Fernando Pacheco; Zhang YulinA series of steel fibre reinforced self-consolidating concrete (SFRSCC) beams have been tested to investigate the influence of steel fibres and the combined effect of fibres and stirrups on the deflection and cracking, ultimate loads and failure pattern. The experiment indicates that the shear strength increases clearly with the increasing of fibre content. The combination of steel fibres and stirrups demonstra...
Arbitrariness of Jordan structure in factorization : the geometric multiplicity...
Johnson, Charles R.; Lewis, Drew; Zhang YulinFor the problem of which Jordan forms are possible for n × n complex matrices A, B and C, when A = BC, geometric multiplicity restrictions are given for the eigenvalues of the three matrices. Together with the obvious determinantal condition on the eigenvalues, these necessary conditions are shown to be sufficient for the problem when n < 4, but not for n ≥ 4. Some basic observations about the problem are given...
Structure-preserving schur methods for computing square roots of real skew-hami...
Liu Zhongyun; Zhang Yulin; Ferreira, Carla; Ralha, RuiThe contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W. Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W, skew-Hamiltonian and Hamilt...
Further geometric restrictions on jordan structure in matrix factorization
Johnson, Charles R.; Lewis, Drew; Zhang YulinIt is known that a nonsingular, nonscalar, n-by-n complex matrix A may be factored as A = BC, in which the spectra of B and C are arbitrary, subject to det(A) = det(B)det(C). It has been shown that when two matrices have eigenvalues of high geometric multiplicity, this restricts the possible Jordan structure of the third. We demonstrate a previously unknown restriction on the Jordan structures of B and C. Furth...
On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks
Zhang Yulin; Liu Zhongyun; Ferreira, Carla; Ralha, RuiWe propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized centrosymmetric ma...
On the possible ranks among matrices with a given pattern
Johnson, Charles R.; Zhang YulinGiven are tight upper and lower bounds for the minimum rank among all matrices with a prescribed zero-nonzero pattern. The upper bound is based upon solving for a matrix with a given null space and, with optimal choices, produces the correct minimum rank. It leads to simple, but often accurate, bounds based upon overt statistics of the pattern. The lower bound is also conceptually simple. Often, the lower and a...
The jordan form problem for C=AB : the balanced, diagonalizable case
Johnson, Charles R.; Zhang YulinWe consider a key case in the fundamental and substantial prob- lem of the possible Jordan canonical forms of A;B;C \in Mn(F) when C = AB. If A \in M2k(F) (respectively B;C \in M2k(F) ) is diagonalizable with two distinct eigenvalues a1; a2 (respectively b1; b2, and c1; c2), each with multiplicity k, and when C = AB, all possibilities for a1; a2; b1; b2; c1; c2 are characterized. The possibilities are much more...
The reconstruction of an hermitian Toeplitz matrices with prescribed eigenpairs
Liu Zhongyun; Chen, Lu; Zhang YulinIn this paper we concern the reconstruction of an hermitian Toeplitz matrices with prescribed eigenpairs. Based on the fact that every centrohermitian matrix can be re- duced to a real matrix by a simple similarity transformation, we rst consider the eigenstructure of hermitian Toeplitz matrices and then discuss a related reconstruction problem. We show that the di- mension of the subspace of hermitian Toeplit...
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