Results 101 to 110 of about 36,359 (205)
ON THE SENSITIVITY OF THE SOLUTION OF THE GENERALIZED LYAPUNOV EQUATION [PDF]
Korean Journal of Mathematics, 2013 Summary: Some results on the sensitivity of the solution of the generalized Lyapunov equation \[ A^{n-1}X + A^{n-2}XA^{\ast} + \cdots + X (A^{\ast})^{n-1} = B \] are shown follow easily from well-known theorems in functional analysis.
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International Journal for Numerical Methods in Engineering, Volume 127, Issue 7, 15 April 2026.ABSTRACT In this article, we propose a novel numerical framework for the non‐isothermal Cahn–Hilliard–Navier–Stokes two‐phase flow system, which couples the incompressible Navier–Stokes equations, the Cahn–Hilliard phase‐field equation, and the heat transport equation to capture temperature‐dependent two‐phase flow dynamics.
Guang‐An Zou +4 more
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Laguerre-Based Frequency-Limited Balanced Truncation of Discrete-Time Systems
MathematicsThis paper introduces a novel model order reduction (MOR) method for linear discrete-time systems, focusing on frequency-limited balanced truncation (BT) techniques. By leveraging Laguerre functions, we develop two efficient MOR algorithms that avoid the
Zhou Song, Qiu-Yan Song, Umair Zulfiqar
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Stability and inertia theorems for generalized Lyapunov equations
Linear Algebra and its Applications, 2002 The author considers the continuous-time Lyapunov equation \(E^*XA+A^*XE=-G\) and its discrete-time analog \(A^*XA-E^*XE=-G\) with given matrices \(E\), \(A\), \(G\) and unknown matrix \(X\). Such equations arise in control problems, stability theory for differential and difference equations and in problems of spectral dichotomy.
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Journal of MathematicsA new negative-order form of the 3+1-dimensional Calogero–Bogoyavlenskii–Schiff equation is examined in this investigation. This equation plays an important role in accurately describing the thermodynamic properties of mixtures, particularly in chemical ...
Ulviye Demirbilek +5 more
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Integrability and chaotic dynamics in nonlinear dispersive stochastic model
Results in Applied MathematicsThis paper focuses on obtaining exact solutions and dynamical analysis of the stochastic real-valued Ginzburg–Landau equation driven by multiplicative Itô noise.
Muhammad Aziz-ur-Rehman +3 more
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EntropyBecause the introduction of a vibro-impact structure can widen the bandwidth and improve the harvesting efficiency of the vibration energy harvesting (VEH) systems, an analytical method for a VEH system based on vibro-impact is proposed to employ the ...
Li Liu, Lili Tian, Meng Su, Hongge Yue
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Numerical solution and perturbation theory for generalized Lyapunov equations
Linear Algebra and its Applications, 2002 The numerical solution and a perturbation theory for the generalized continuous-time Lyapunov equation \(E^*XA+ A^*XE= -G\) with a singular matrix \(E\) are presented. This equation may not have solutions and even if a solution exists, it is, in general, not unique. Generalizations of the Bartels-Stewart and Hammarling methods are proposed to compute a
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Analytical and dynamical analysis of nonlinear Riemann wave equation in plasma systems
Arab Journal of Basic and Applied SciencesThe Riemann wave equation presents appealing nonlinear equations applicable in sea-water and tsunami wave propagation, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, and homogeneous stationary media.
Adil Jhangeer +4 more
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Generalized Lyapunov–Schmidt reduction for parametrized equations at near singular points
Linear Algebra and its Applications, 2001 The solution manifold to the nonlinear equation \(F(\lambda,u)= 0\) in a neighbourhood of an approximate zero is investigated. Here, \(F\) is a sufficiently smooth nonlinear mapping with values in a Banach space, \(\lambda\) is a real-valued vector, and \(u\) is element of another Banach space.
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