281 research outputs found

    Effective partitioning method for computing weighted Moore-Penrose inverse

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    We introduce a method and an algorithm for computing the weighted Moore-Penrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are generalizations of algorithms developed in [M.B. Tasic, P.S. Stanimirovic, M.D. Petkovic, Symbolic computation of weighted Moore-Penrose inverse using partitioning method, Appl. Math. Comput. 189 (2007) 615-640] to multiple-variable rational and polynomial matrices and improvements of these algorithms on sparse matrices. Also, these methods are generalizations of the partitioning method for computing the Moore-Penrose inverse of rational and polynomial matrices introduced in [P.S. Stanimirovic, M.B. Tasic, Partitioning method for rational and polynomial matrices, Appl. Math. Comput. 155 (2004) 137-163; M.D. Petkovic, P.S. Stanimirovic, Symbolic computation of the Moore-Penrose inverse using partitioning method, Internat. J. Comput. Math. 82 (2005) 355-367] to the case of weighted Moore-Penrose inverse. Algorithms are implemented in the symbolic computational package MATHEMATICA

    Computation of generalized inverses using Php/MySql environment

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    The main aim of this paper is to develop a client/server-based model for computing the weighted Moore-Penrose inverse using the partitioning method as well as for storage of generated results. The web application is developed in the PHP/MySQL environment. The source code is open and free for testing by using a web browser. Influence of different matrix representations and storage systems on the computational time is investigated. The CPU time for searching the previously stored pseudo-inverses is compared with the CPU time spent for new computation of the same inverses.Comment: International Journal of Computer Mathematics, Volume 88, Issue 11, 201

    Computation of generalized inverses by using the LDL∗ decomposition

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    AbstractAn efficient algorithm, based on the LDL∗ factorization, for computing {1,2,3} and {1,2,4} inverses and the Moore–Penrose inverse of a given rational matrix A, is developed. We consider matrix products A∗A and AA∗ and corresponding LDL∗ factorizations in order to compute the generalized inverse of A. By considering the matrix products (R∗A)†R∗ and T∗(AT∗)†, where R and T are arbitrary rational matrices with appropriate dimensions and ranks, we characterize classes A{1,2,3} and A{1,2,4}. Some evaluation times for our algorithm are compared with corresponding times for several known algorithms for computing the Moore–Penrose inverse

    Representations and symbolic computation of generalized inverses over fields

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    This paper investigates representations of outer matrix inverses with prescribed range and/or none space in terms of inner inverses. Further, required inner inverses are computed as solutions of appropriate linear matrix equations (LME). In this way, algorithms for computing outer inverses are derived using solutions of appropriately defined LME. Using symbolic solutions to these matrix equations it is possible to derive corresponding algorithms in appropriate computer algebra systems. In addition, we give sufficient conditions to ensure the proper specialization of the presented representations. As a consequence, we derive algorithms to deal with outer inverses with prescribed range and/or none space and with meromorphic functional entries.Agencia Estatal de investigaciónUniversidad de Alcal

    Representations and geometrical properties of generalized inverses over fields

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    In this paper, as a generalization of Urquhart’s formulas, we present a full description of the sets of inner inverses and (B, C)-inverses over an arbitrary field. In addition, identifying the matrix vector space with an affine space, we analyze geometrical properties of the main generalized inverse sets. We prove that the set of inner inverses, and the set of (B, C)-inverses, form affine subspaces and we study their dimensions. Furthermore, under some hypotheses, we prove that the set of outer inverses is not an affine subspace but it is an affine algebraic variety. We also provide lower and upper bounds for the dimension of the outer inverse set.Agencia Estatal de InvestigaciónUniversidad de Alcal

    Regression and Singular Value Decomposition in Dynamic Graphs

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    Most of real-world graphs are {\em dynamic}, i.e., they change over time. However, while problems such as regression and Singular Value Decomposition (SVD) have been studied for {\em static} graphs, they have not been investigated for {\em dynamic} graphs, yet. In this paper, we introduce, motivate and study regression and SVD over dynamic graphs. First, we present the notion of {\em update-efficient matrix embedding} that defines the conditions sufficient for a matrix embedding to be used for the dynamic graph regression problem (under l2l_2 norm). We prove that given an n×mn \times m update-efficient matrix embedding (e.g., adjacency matrix), after an update operation in the graph, the optimal solution of the graph regression problem for the revised graph can be computed in O(nm)O(nm) time. We also study dynamic graph regression under least absolute deviation. Then, we characterize a class of matrix embeddings that can be used to efficiently update SVD of a dynamic graph. For adjacency matrix and Laplacian matrix, we study those graph update operations for which SVD (and low rank approximation) can be updated efficiently

    Steering Law Design for Redundant Single Gimbal Control Moment Gyro Systems

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    The correspondence between robotic manipulators and single gimbal Control Moment Gyro (CMG) systems was exploited to aid in the understanding and design of single gimbal CMG Steering laws. A test for null motion near a singular CMG configuration was derived which is able to distinguish between escapable and unescapable singular states. Detailed analysis of the Jacobian matrix null-space was performed and results were used to develop and test a variety of single gimbal CMG steering laws. Computer simulations showed that all existing singularity avoidance methods are unable to avoid Elliptic internal singularities. A new null motion algorithm using the Moore-Penrose pseudoinverse, however, was shown by simulation to avoid Elliptic type singularities under certain conditions. The SR-inverse, with appropriate null motion was proposed as a general approach to singularity avoidance, because of its ability to avoid singularities through limited introduction of torque error. Simulation results confirmed the superior performance of this method compared to the other available and proposed pseudoinverse-based Steering laws

    On the constraints violation in forward dynamics of multibody systems

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    It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method.The first author expresses his gratitude to the Portuguese Foundation for Science and Technology through the PhD grant (PD/BD/114154/2016). This work has been supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio
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