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Showing 1 to 19 of 19 for “"matrix exponential"”.
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The computation of matrix functions in particular, the matrix exponential
Matrix functions in general are an interesting area in matrix analysis and are used in many areas of linear algebra and arise in numerous applications in science and engineering. We consider how to define matrix functions and how to compute matrix functions. To be concrete, we pay particular …
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Optimization of Handover, Survivability, Multi-Connectivity and Secure Slicing in 5G Cellular Networks using Matrix Exponential Models and Machine Learning
… and secure network slicing using matrix exponentials and machine learning techniques. We propose matrix exponential (ME) modeling of handover arrivals with the potential to much more accurately characterize arrivals and prioritize resource allocation for handovers, especially …
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Accelerating Finite State Projection through General Purpose Graphics Processing
… master equation. The algorithm utilizes the matrix exponential function, and so the algorithm’s performance suffers when it is applied to large problems. Other work has been done to reduce the size of the exponentiation through mathematical simplifications, but efficiently exponentiating a …
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Graph diffusions and matrix functions: fast algorithms and localization results
… Whereas many standard graph algorithms rely on matrix-vector operations that require exploring the entire graph, this thesis is concerned with graph algorithms that are local (that explore only the graph region near the nodes of interest) as well as the localized behavior of global algorithms. …
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Modeling and numerical methods for power electronic devices
… Computation time is reduced by calculating the matrix exponential using a decomposition method. With an efficient means of computing the matrix exponential, switching instances are updated reliably from previous computed values, providing a very quick means for event-detection state vector …
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Sequential estimation of optimal age replacement policies when distribution of lifetimes is phase type.
… type distributions and the distributions include matrix exponential terms, the parameters are in general difficult to estimate. A specific case where the phase type distribution has initial probability vector a=(1,0,0) is studied for different sample sizes and compared with a similar nonparametric …
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Aeroelasticity of Morphing Wings Using Neural Networks
… for each time interval is in the form of a matrix exponential and hence this technique is termed as Matrix Exponential time marching. Using this time marching technique, Artificial Neural Networks can be trained to represent the dynamic behavior of any linearly time varying system. In order …
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A perturbation approach to control of rotational/translational maneuvers of flexible space vehicles
… value problem is accomplished through the use of matrix exponential functions. Maneuvers which involve the translational degrees of freedom, are described by nonlinear equations. The solution method presented is a algorithm that generates successive approximations similar to quasi-linearization. A …
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Exponential integrators: tensor structured problems and applications
… integrate such systems involves using exponential integrators. In general, these kinds of schemes do not require the solution of (non)linear systems but rather the action of the matrix exponential and of some specific exponential-like functions (known in the literature as φ-functions). …
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Fast time- and frequency-domain finite-element methods for electromagnetic analysis
… methods, explicit methods can avoid solving a matrix equation. However, their time step is traditionally restricted by the space step for ensuring the stability of a time-domain simulation. Therefore, making explicit time-domain methods unconditionally stable is important to accelerate the …
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Numerical simulations in nuclear magnetic resonance : theory and applications
… of the propagator via Chebyshev expansion of the matrix exponential, explicit utilization of the sparsity of the Hamiltonian, and a novel methodology for the simulation of solid-state NMR experiments. We also describe SPINEVOLUTION, a highly optimized computer program developed based on these …
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Advanced Time Integration Methods with Applications to Simulation, Inverse Problems, and Uncertainty Quantification
… a posteriori error framework. We extend exponential propagation iterative methods of Runge-Kutta type (EPIRK) by [Tokman, JCP 2011], to build EPIRK-W and EPIRK-K time integration methods that admit approximate Jacobians in the matrix-exponential like operations. EPIRK-W methods extend the …
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Numerical methods for systems of highly oscillatory ordinary differential equations
… approach and the Filon-type method, to solve matrix exponential. The second method, we call it the WRF method, a combination of the Filon-type method and the waveform relaxation methods, for solving highly oscillatory non-linear systems. Finally, completing the theory, we show that the …
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A generalized optimization methodology for isotope management
… annealing optimization methodology to a simple matrix exponential depletion code written in Fortran using cross sections generated from the SCALE code system. Since flux spectra cannot be shaped arbitrarily, the second half of this research applied the same methodology to material composition of …
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Developing and Utilizing Multivariate Stochastic Wireless Channel Models
… wasteful and unnecessary, so it is shown using matrix exponential distributions how with low complexity to duplicate only when necessary. The results indicate that up to 50% of the resources at the duplicating base station can be liberated whilst meeting the target reliability measure.
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Exponential Integrators for the Incompressible Navier-Stokes Equations
… functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is …
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Autonomous Space Surveillance for Arbitrary Domains
… of motion are developed with a semi-analytical matrix exponential method. The motion models are tested on various cislunar orbit geometries for both the elliptical restricted three-body problem (ER3BP) and the circular restricted three-body problem (CR3BP) through MATLAB simulations. The linear …
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Combined multispectral/hyperspectral remote sensing of tropospheric aerosols for quantification of their direct radiative effect
… simulation of measurements. Our approach is matrix operator based and uses the Padé approximation for the matrix exponential to evaluate the homogeneous solution. It is shown that the method is two to four times faster than the standard and efficient discrete ordinate technique and is …
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Controllability, Observability and Realizability
… systems, time-varying systems, and first-order matrix Sylvester systems. Examples and sample computed calculations are provided for both uncontrolled and controlled systems. We also develop a new method for computing the approximate values of matrix exponentials, and use this to estimate …