7 research outputs found
Solutions to an inverse monic quadratic eigenvalue problem
AbstractGiven n+1 pairs of complex numbers and vectors (closed under complex conjugation), the inverse quadratic eigenvalue problem is to construct real symmetric or anti-symmetric matrix C and real symmetric matrix K of size n脳n so that the quadratic pencil Q(位)=位2In+位C+K has the given n+1 pairs as eigenpairs. Necessary and sufficient conditions under which this quadratic inverse eigenvalue problem is solvable are obtained. Numerical algorithms for solving the problem are developed. Numerical examples illustrating these solutions are presented
Stiffness matrix modification with vibration test data by displacement feedback technique
A no spill-over method is developed which uses measured normal modes and natural frequencies to adjust a structural dynamics model in light of displacement feedback technique. By the method, the required displacement feedback gain matrix is determined, and thus the updated stiffness matrix which satisfies the characteristic equation is found in the Frobenius norm sense and the large number of unmeasured high-order modal data of the original model is preserved. The method directly identifies, without iteration, and the solution of this problem is of a compact expression. The numerical example shows that the modal measured data are better incorporated into the updated model
Mathematical and physical aspects of complex symmetric operators
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugate-linear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics, and complex variables
ABS-Based Direct Method for Solving Complex Systems of Linear Equations
Efficient solution of linear systems of equations is one of the central topics of numerical
computation. Linear systems with complex coefficients arise from various physics and quantum
chemistry problems. In this paper, we propose a novel ABS-based algorithm, which is able to solve
complex systems of linear equations. Theoretical analysis is given to highlight the basic features of
our new algorithm. Four variants of our algorithm were also implemented and intensively tested
on randomly generated full and sparse matrices and real-life problems. The results of numerical
experiments reveal that our ABS-based algorithm is able to compute the solution with high accuracy.
The performance of our algorithm was compared with a commercially available software, Matlab鈥檚
mldivide (\) algorithm. Our algorithm outperformed the Matlab algorithm in most cases in terms of
computational accuracy. These results expand the practical usefulness of our algorithm