Results 1 to 10 of about 72,021 (274)

Lie algebras of differentiations of linear algebras over a field

Дифференциальная геометрия многообразий фигур, 2021
In this paper, we study a system of linear equations that define the Lie algebra of differentiations DerA of an arbitrary finite-dimensional linear algebra over a field.
A. Ya. Sultanov, M.V. Glebova, O.V. Bolotnikova   +2 more
doaj   +3 more sources

Differentiation of linear algebras with a unit over a field

Дифференциальная геометрия многообразий фигур, 2023
Linear algebras over a given field arise when studying various problems of algebra, analysis and geometry. The operation of differentiation, which originated in mathematical analysis, was transferred to the theory of linear algebras over a field, as well
A.Ya. Sultanov, M. V. Glebova, G. A. Sultanova   +2 more
doaj   +2 more sources

DIFFERENTIATION OF POLYNOMIALS IN SEVERAL VARIABLES OVER GALOIS FIELDS OF FUZZY CARDINALITY AND APPLICATIONS TO REED-MULLER CODES

Advanced Engineering Research, 2018
Introduction. Polynomials in several variables over Galois fields provide the basis for the Reed-Muller coding theory, and are also used  in a number of cryptographic problems.
V. M. Deundyak, N. S. Mogilevskaya
doaj   +2 more sources

Non-linear estimation is easy [PDF]

International journal of Modeling, identification and control, 2007
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation.
Fliess, Michel, Join, Cédric, Sira-Ramirez, Hebertt   +2 more
core   +6 more sources

On derivations of linear algebras of a special type

Дифференциальная геометрия многообразий фигур
In this work, Lie algebras of differentiation of linear algebra, the op­eration of multiplication in which is defined using a linear form and two fixed elements of the main field are studied. In the first part of the work, a definition of differentiation
A. Ya. Sultanov , O. A. Monakhova, O. V. Bolotnikova   +2 more
doaj   +2 more sources

Exploring parameter dependence of atomic minima with implicit differentiation

npj Computational Materials
Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst backpropagation has ...
Ivan Maliyov, Petr Grigorev, Thomas D. Swinburne   +2 more
doaj   +2 more sources

Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory

Sensors
This paper presents a sensor fusion method for navigation of unmanned underwater vehicles. The method combines Lie theory into Kalman filter to estimate and compensate for the misalignment between the sensors: inertial navigation system and Doppler ...
Da Bin Jeong, Nak Yong Ko
doaj   +2 more sources

CoLA: Exploiting Compositional Structure for Automatic and Efficient Numerical Linear Algebra [PDF]

Neural Information Processing Systems, 2023
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation.
Andres Potapczynski, Marc Finzi, Geoff Pleiss, Andrew Gordon Wilson   +3 more
semanticscholar   +1 more source

Solving Nonlinear Multi-Order Fractional Differential Equations Using Bernstein Polynomials

IEEE Access, 2023
This paper introduces two novel methods for solving multi-order fractional differential equations using Bernstein polynomials. The first method, referred to as the fractional operational matrix of differentiation of Bernstein polynomials, is employed to ...
Shahad Adil Taher Algazaa, Jamshid Saeidian   +1 more
doaj   +1 more source

AUTOMATION OF TENSOR CALCULATIONS BASED ON NEURAL NETWORKS

Современная наука и инновации, 2022
Tensor calculus is a necessary tool in various natural sciences.
A. N. Makokha, T. E. Tyshlyar
doaj   +1 more source