Related papers: Numerical Performance of Abs Codes for Nonlinear S…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…
Computers are nonlinear dynamical systems that exhibit complex and sometimes even chaotic behavior. The models used in the computer systems community, however, are linear. This paper is an exploration of that disconnect: when linear models…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
The focus of this thesis is on the applications of nonlinear dynamical systems in bioengineering which are mainly used in large-scale and generally categorised into two groups: (1) dynamical systems from biology (2) dynamical systems for…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
We apply the iterative nonlinear programming method, previously proposed in our earlier work, to optimize Schur test functions and thereby provide refined upper bounds for the norms of integral operators. As an illustration, we derive such…
We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the…
Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves…
We present some results in the analysis of non-compact differential equations on unbounded domains.
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…
Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most…
We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
Linear codes have been an interesting subject of study for many years. Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, a class of three-weight linear codes over Fp…
Twenty years ago the anti-reflective numerical boundary conditions (BCs) were introduced in a context of signal processing and imaging, for increasing the quality of the reconstruction of a blurred signal/image contaminated by noise and for…
In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schr\"odinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the…