Moore–Penrose pseudoinverse
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Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics Open
Perturbation bounds for singular spaces, in particular Wedin’s $\\mathop{\\mathrm{sin}}\\nolimits \\Theta$ theorem, are a fundamental tool in many fields including high-dimensional statistics, machine learning and applied mathematics. In t…
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Pseudoinverse of the Laplacian and best spreader node in a network Open
Determining a set of "important" nodes in a network constitutes a basic endeavor in network science. Inspired by electrical flows in a resistor network, we propose the best conducting node j in a graph G as the minimizer of the diagonal el…
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On Weight-Prioritized Multitask Control of Humanoid Robots Open
International audience
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Characterizations of <i>k</i>-commutative equalities for some outer generalized inverses Open
[EN] In this paper, we present necessary and sufficient conditions for the k-commutative equality , where X is an outer generalized inverse of the square matrix A. Also, we give new representations for core EP, DMP, and CMP inverses of squ…
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Proceedings of the 2017 Federated Conference on Computer Science and Information Systems Open
There are many practical applications based on the Least Square Error (LSE)\napproximation. It is based on a square error minimization 'on a vertical' axis.\nThe LSE method is simple and easy also for analytical purposes. However, if\ndata…
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Inverse optimal control from incomplete trajectory observations Open
This article develops a methodology that enables learning an objective function of an optimal control system from incomplete trajectory observations. The objective function is assumed to be a weighted sum of features (or basis functions) w…
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The general $\phi$-Hermitian solution to mixed pairs of quaternion matrix Sylvester equations Open
Let $\mathbb{H}^{m\times n}$ be the space of $m\times n$ matrices over $\mathbb{H}$, where $\mathbb{H}$ is the real quaternion algebra. Let $A_{\phi}$ be the $n\times m$ matrix obtained by applying $\phi$ entrywise to the transposed matrix…
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Dynamics of a four‐wheeled mobile robot with Mecanum wheels Open
The paper deals with the dynamics of a mobile robot with four Mecanum wheels. For such a system the kinematical rolling conditions lead to non‐holonomic constraints. From the framework of non‐holonomic mechanics Chaplygin's equation is use…
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ON ONE-SIDED (B;C)-INVERSES OF ARBITRARY MATRICES Open
In this article, one-sided $(b, c)$-inverses of arbitrary matrices as well as one-sided inverses along a (not necessarily square) matrix, will be studied. In addition, the $(b, c)$-inverse and the inverse along an element will be also rese…
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The class of<i>m</i>-<i>EP</i>and<i>m</i>-normal matrices Open
The well-known classes of EP matrices and normal matrices are de- \nfined by the matrices that commute with their Moore-Penrose inverse \nand with their conjugate transpose, respectively. This paper investigates \nthe class of m-EP matrice…
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Accurate Delay Estimation for Multisensor Passive Locating Systems Exploiting the Cross-Correlation Between Signals Cross-Correlations Open
The availability of accurate estimates of the delay or time of arrival (TOA) of the incoming signals is of paramount importance for the position estimation in passive radars with multiple receivers. This correspondence aims at improving es…
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Representations and properties of the <i>W</i>-weighted core-EP inverse Open
In this paper, we investigate the weighted core-EP inverse introduced by Ferreyra, Levis and Thome. Several computational representations of the weighted core-EP inverse are obtained in terms of singular-value decomposition, full-rank deco…
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The inverse along an element in rings Open
[EN] Several properties of the inverse along an element are studied in the context of unitary rings. New characterizations of the existence of this inverse are proved. Moreover, the set of all invertible elements along a fixed element is f…
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Sparse Identification of Volterra Models for Power Amplifiers Without Pseudoinverse Computation Open
We present a new formulation of the doubly orthogonal matching pursuit (DOMP) algorithm for the sparse recovery of Volterra series models. The proposal works over the covariance matrices by taking advantage of the orthogonal properties of …
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Development of derivation of inverse Jacobian matrices for 195 6-DOF GSP mechanisms Open
One of the key issues in robotics is finding high-performance manipulator structures. To evaluate the performance of a parallel manipulator, researchers mostly use kinematic performance indices (such as condition number, minimum singular v…
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Space Vectors and Pseudoinverse Matrix Methods for the Radial Force Control in Bearingless Multisector Permanent Magnet Machines Open
Two different approaches to characterize the torque and radial force production in a bearingless multisector permanent magnet machine are presented in this paper. The first method consists of modeling the motor in terms of torque and force…
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Two step imaging reconstruction using truncated pseudoinverse as a preliminary estimate in ultrasound guided diffuse optical tomography Open
Due to the correlated nature of diffused light, the problem of reconstructing optical properties using diffuse optical tomography (DOT) is ill-posed. US-, MRI- or x-ray-guided DOT approaches can reduce the total number of parameters to be …
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Disturbance Accommodating Control Design for Wind Turbines Using Solvability Conditions Open
In this paper, solvability conditions for disturbance accommodating control (DAC) have been discussed and applied on wind turbine controller design in above-rated wind speed to regulate rotor speed and to mitigate turbine structural loads.…
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Reverse order law for the inverse along an element Open
In this paper, we introduce a new concept called left (right) g-MP inverse in a *-monoid. The relations of this type of generalized inverse with left inverse along an element are investigated. Also, the reverse order law for the inverse al…
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An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators Open
Different from traditional redundant manipulators, the redundant manipulators used in the surgical environment require the end effector (EE) to have high pose (position and orientation) accuracy to ensure the smooth progress of the operati…
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Zeroing Neural Network for Pseudoinversion of an Arbitrary Time-Varying Matrix Based on Singular Value Decomposition Open
Many researchers have investigated the time-varying (TV) matrix pseudoinverse problem in recent years, for its importance in addressing TV problems in science and engineering. In this paper, the problem of calculating the inverse or pseudo…
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The inverse kinematics of a 7R 6-degree-of-freedom robot with non-spherical wrist Open
The 7R 6-degree-of-freedom robots with hollow non-spherical wrist have been proven more suitable to spray painting. However, the inverse kinematics of this robot is still imperfect due to the coupling between position and orientation of th…
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A Noise-Acceptable ZNN for Computing Complex-Valued Time-Dependent Matrix Pseudoinverse Open
The issue of complex-valued time-dependent pseudoinverse often exists in science and engineering fields. In the existing studies, many models were presented for solving complex-valued time-dependent pseudoinverse in the noiseless environme…
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Evolutionary Computation Based Real-time Robot Arm Path-planning Using Beetle Antennae Search Open
This paper presents a model-free real-time kinematic tracking controller for a redundant manipulator. Redundant manipulators are common in industrial applications because of the flexibility and dexterity they get from redundant joints. How…
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Forward and Inverse Kinematics Using Pseudoinverse and Transposition Method for Robotic Arm DOBOT Open
Kinematic structure of the DOBOT manipulator is presented in this chapter. Joint coordinates and end-effector coordinates of the manipulator are functions of independent coordinates, i.e., joint parameters. This chapter explained forward k…
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Generalized Inverses Estimations by Means of Iterative Methods with Memory Open
A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A. For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the matrix is singular, an…
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Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics Open
Perturbation bounds for singular spaces, in particular Wedin's $\sin Θ$ theorem, are a fundamental tool in many fields including high-dimensional statistics, machine learning, and applied mathematics. In this paper, we establish separate p…
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Dual group inverses of dual matrices and their applications in solving systems of linear dual equations Open
In this paper, we study a kind of dual generalized inverses of dual matrices, which is called the dual group inverse. Some necessary and sufficient conditions for a dual matrix to have the dual group inverse are given. If one of these cond…
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Quantum-inspired algorithms for solving low-rank linear equation systems with logarithmic dependence on the dimension Open
We present two efficient classical analogues of the quantum matrix inversion algorithm [16] for low-rank matrices. Inspired by recent work of Tang [27], assuming length-square sampling access to input data, we implement the pseudoinverse o…
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Linearly Convergent Randomized Iterative Methods for Computing the Pseudoinverse Open
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the p…