Search results for "Matrix"
showing 10 items of 3205 documents
Inversion of matrix pencils for generalized systems
1993
Abstract This paper clarifies the nature of the Leverrier-Faddeev algorithm for generalized and state-space systems. It presents useful diagrams for recursive computation of the coefficients of the characteristic polynomial and the coefficient matrices of the adjoint matrix for various matrix pencils. A simplified case covers recursive equations and diagrams for inversion of the second-order matrix pencil (Es2 + A1s + A0) where E may be singular. The appendix provides two examples of mechanical and heat exchange systems which can be described by the generalized models.
Unary Probabilistic and Quantum Automata on Promise Problems
2015
We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs can be exponentially more succinct than DFAs.
Observer-based control design for a class of nonlinear systems subject to unknown inputs: LMI approach
2015
This paper deals with the problem of observer-based controller design for a class of nonlinear systems subject to unknown inputs. A novel method is presented to design a controller using estimated state variables which guarantees all the state variables of the closed-loop system converge to the vicinity of the origin and stay there forever. This is done via satisfying several sufficient conditions in terms of nonlinear matrix inequalities. In light of linear algebra, particularly matrix decompositions, the achieved conditions will be converted to a Linear Matrix Inequality (LMI) problem to facilitate the procedure of computing the observer and controller gains. Finally, the effectiveness of…
Magnus and Fer expansions for matrix differential equations: the convergence problem
1998
Approximate solutions of matrix linear differential equations by matrix exponentials are considered. In particular, the convergence issue of Magnus and Fer expansions is treated. Upper bounds for the convergence radius in terms of the norm of the defining matrix of the system are obtained. The very few previously published bounds are improved. Bounds to the error of approximate solutions are also reported. All results are based just on algebraic manipulations of the recursive relation of the expansion generators.
Joint Graph Learning and Signal Recovery via Kalman Filter for Multivariate Auto-Regressive Processes
2018
In this paper, an adaptive Kalman filter algorithm is proposed for simultaneous graph topology learning and graph signal recovery from noisy time series. Each time series corresponds to one node of the graph and underlying graph edges express the causality among nodes. We assume that graph signals are generated via a multivariate auto-regressive processes (MAR), generated by an innovation noise and graph weight matrices. Then we relate the state transition matrix of Kalman filter to the graph weight matrices since both of them can play the role of signal propagation and transition. Our proposed Kalman filter for MAR processes, called KF-MAR, runs three main steps; prediction, update, and le…
On the geometry of the characteristic class of a star product on a symplectic manifold
2001
The characteristic class of a star product on a symplectic manifold appears as the class of a deformation of a given symplectic connection, as described by Fedosov. In contrast, one usually thinks of the characteristic class of a star product as the class of a deformation of the Poisson structure (as in Kontsevich's work). In this paper, we present, in the symplectic framework, a natural procedure for constructing a star product by directly quantizing a deformation of the symplectic structure. Basically, in Fedosov's recursive formula for the star product with zero characteristic class, we replace the symplectic structure by one of its formal deformations in the parameter $\hbar$. We then s…
Derived variables calculated from similar joint responses: some characteristics and examples
1995
Abstract A technique (Cox and Wermuth, 1992) is reviewed for finding linear combinations of a set of response variables having special relations of linear conditional independence with a set of explanatory variables. A theorem in linear algebra is used both to examine conditions in which the derived variables take a specially simple form and lead to reduced computations. Examples are discussed of medical and psychological investigations in which the method has aided interpretation.
Tests against stationary and explosive alternatives in vector autoregressive models
2008
. The article proposes new tests for the number of unit roots in vector autoregressive models based on the eigenvalues of the companion matrix. Both stationary and explosive alternatives are considered. The limiting distributions of test statistics depend only on the number of unit roots. Size and power are investigated, and it is found that the new test against some stationary alternatives compares favourably with the widely used likelihood ratio test for the cointegrating rank. The powers are prominently higher against explosive than against stationary alternatives. Some empirical examples are provided to show how to use the new tests with real data.
The asymptotic covariance matrix of the Oja median
2003
The Oja median, based on a sample of multivariate data, is an affine equivariant estimate of the centre of the distribution. It reduces to the sample median in one dimension and has several nice robustness and efficiency properties. We develop different representations of its asymptotic variance and discuss ways to estimate this quantity. We consider symmetric multivariate models and also the more narrow elliptical models. A small simulation study is included to compare finite sample results to the asymptotic formulas.
On Association Models Defined over Independence Graphs
1998
Conditions on joint distributions are given under which two variables will be conditionally associated whenever an independence graph does not imply a corresponding conditional independence statement. To this end the notions of parametric cancellation, of stable paths and of quasi-linear models are discussed in some detail.