More efficient use of determinants to solve transcendental structural eigenvalue problems reliably

Transcendental inverse eigenvalue problems in damage parameter estimation

Summary 1. Occupancy estimation and modelling based on detection‐nondetection data provide an effective way of exploring change in a species’ distribution across time and space in cases where the species is not always detected with certainty. Today, many monitoring programmes target multiple species, or life stages within a species, requiring the use of multiple detection methods. When multiple methods or devices are used at the same sample sites, animals can be detected by more than one method. 2. We develop occupancy models for multiple detection methods that permit simultaneous use of data from all methods for inference about method-specific detection probabilities. Moreover, the approach permits estimation of occupancy at two spatial scales: the larger scale corresponds to species’ use of a sample unit, whereas the smaller scale corresponds to presence of the species at the local sample station or site. 3. We apply the models to data collected on two different vertebrate species: striped skunks Mephitis mephitis and red salamanders Pseudotriton ruber . For striped skunks, large-scale occupancy estimates were consistent between two sampling seasons. Small-scale occupancy probabilities were slightly lower in the late winter/spring when skunks tend to conserve energy, and movements are limited to males in search of females for breeding. There was strong evidence of method-specific detection probabilities for skunks. As anticipated, large- and small-scale occupancy areas completely overlapped for red salamanders. The analyses provided weak evidence of method-specific detection probabilities for this species. 4. Synthesis and applications. Increasingly, many studies are utilizing multiple detection methods at sampling locations. The modelling approach presented here makes efficient use of detections from multiple methods to estimate occupancy probabilities at two spatial scales and to compare detection probabilities associated with different detection methods. The models can be viewed as another variation of Pollock’s robust design and may be applicable to a wide variety of scenarios where species occur in an area but are not always near the sampled locations. The estimation approach is likely to be especially useful in multispecies conservation programmes by providing efficient estimates using multiple detection devices and by providing device-specific detection probability estimates for use in survey design.

An incremental compiler, in response to a program change, recompiles only the part of the program affected by the change, resulting in more efficient use of system resources and in improved response time. Current incremental programming environments based on compilation do not combine a small incremental unit for recompilation with sophisticated local and global register allocation schemes. This dissertation studies the problems of incrementally allocating local and global registers and generating target code in response to program edits. The unit of change is an intermediate code statement, and the target code that is produced incrementally utilizes registers as efficiently as a non-incremental target code generator that uses the same register allocation heuristics. The first step in the design of an incremental target code generator is an analysis of the effects of program edits on existing local and global register allocation. From the analysis, a model of register histories is constructed that maintains the ideal and the actual register allocation for the program. The model is designed to be independent of the local and global register allocation heuristics that are used. However, it is particularly useful for the incremental allocation of both local and global registers using graph coloring. Using the analysis and the model, incremental techniques for allocating registers and generating target code are developed. To provide insight into the performance of the incremental target code generator, both incremental and non-incremental systems are implemented. Their performances are compared both in terms of the quality of the target code that is produced and in the time it takes to make changes incrementally rather than by completely regenerating the target code. The results of the experiments indicate that the same high-quality target code that is produced non-incrementally can be produced incrementally. Under certain conditions, the savings for incremental incorporation of changes are considerable. The savings in time depend on the amount of code that is changed and on the amount of disruption to the register allocation. For test cases that involve changes to global register allocation, the savings in time range from 34 to 96% when up to 16% of the program is changed.

Theory of curve crossing and curve veering phenomena is well known in structural dynamics, but only few papers have used test bench to demonstrate and validate this eigenvalues behaviour. The aim of this paper is to present a theoretical and experimental analysis on a nonsymmetric experimental structure with eigenvalues curve veering and crossing phenomena. Starting from literature examples, detailed numerical models on lumped parameters systems and continuous systems with coincident and/or close eigenvalues are examined in order to developed a numerical FE model suitable to describe a tunable and simple test rig with coincident eigenvalues and curve veering phenomena without symmetric properties or completely uncoupled dynamic systems. The test bench is made of simple beams and masses properly linked together. The angle of an intermediate beam is used as tunable physical parameter to vary the eigenvalues of the system and to couple two bending modes or bending and torsional modes. Numerical and experimental results are compared, and sensitivity of mode shapes to variation of system parameters is discussed. KeywordsMode ShapeTest BenchBeam ElementTorsional ModeModal Assurance CriterionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The main goal of this article is the study of the convergence and optimality properties of adaptive finiteelement methods (AFEMs) for Steklov eigenvalue problems. These problems arise, for example, in the analysis of the stability of mechanical oscillators immersed in a viscous fluid (see Conca et al., 1995 and the references therein) or in the study of vibration modes of a structure interacting with an incompressible fluid (Bermudez et al., 2000). Finite-element approximations for these problems have been widely used and analysed under a general framework. AFEMs make efficient use of the computational resources, and for certain problems AFEMs are even indispensable for their numerical resolvability. The ultimate goal of adaptive methods is to equidistribute the error and the computational effort to obtain a sequence of meshes with optimal complexity. Historically, the first step to prove optimality has been to understand the convergence of adaptive methods. A basic result for the convergence of linear problems was presented in Morin et al. (2008), where very general conditions on the linear problems and on the ingredients of the AFEM that guarantee convergence were stated. Following these ideas, the (plain) convergence of an AFEM for elliptic eigenvalue problems was proved in Garau et al. (2009). The optimality of an AFEM using Dorfler’s marking strategy (Dorfler, 1996) was proved by Stevenson (2007) and Cascon et al. (2008) for linear elliptic problems. The linear convergence of an AFEM for elliptic eigenvalue problems was proved in Giani & Graham (2009) when considering the approximation of simple eigenvalues, provided that the initial mesh is sufficiently fine, and an improvement of this AFEM including optimality was presented in Dai et al. (2008). In this article we consider the Steklov eigenvalue problem that consists of finding λ ∈ R and u 6≡ 0 such that −∇ ∙ (A∇u)+ cu = 0 in Ω, (A∇u) ∙ −→n = λρu on ∂Ω,

A direct digital frequency synthesizer (DDFS) based on a non-equal division parabolic polynomial interpolation method is proposed in this paper. To attain high spurious free dynamic range (SDRF) and reduce area cost, a parabolic polynomial interpolation method is adopted in the proposed design to replace conventional ROM-based phase-to-sine mapper methods. Particularly, the left 1/4 of the phase range is approximated using a low-curvature parabolic curve. The proposed design is manufactured using a standard 0.18 μm CMOS technology. The maximum output frequency is 50 MHz, the core area is 1.4528 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and the spurious free dynamic range (SFDR) is 68.67 dBc. The proposed DDFS outperforms prior works' SFDR and energy efficiency.

An adaptive inverse iteration algorithm using interpolating multiwavelets for structural eigenvalue problems

Badly-scaled matrices or matrix pencils can reduce the reliability and accuracy of computed results for various numerical problems, including the computation of spectra and bases of invariant or deflating subspaces, which are used in many basic procedures for optimal and robust control, model reduction, spectral factorization, and other domains. Standard balancing techniques can often improve the results, but sometimes the solution of the scaled problem is much worse than that for the original problem. This paper presents an improved balancing technique for general or structured matrices and matrix pencils, and illustrates its good performance in solving eigenvalue problems and algebraic Riccati equations for large sets of examples from well-known benchmark collections.

In linear stability analysis of a large-scale dynamical system, we need to compute the rightmost eigenvalue(s) for a series of large generalized eigenvalue problems. Existing iterative eigenvalue solvers are not robust when no estimate of the rightmost eigenvalue(s) is available. In this study, we show that such an estimate can be obtained from Lyapunov inverse iteration applied to a special eigenvalue problem of Lyapunov structure. An analysis that explains the fast convergence of this algorithm observed in numerical experiments is provided, based on which we propose a more efficient and robust algorithm. Furthermore, we generalize the same idea to a deflated version of this Lyapunov eigenvalue problem and propose an algorithm that computes a few rightmost eigenvalues for the eigenvalue problems arising from linear stability analysis.

Mode localization and eigenvalue loci veering phenomena in disordered structures

The speedy computation of eigenvalue problems is the key point in structure dynamics. In this paper, by combining transfer matrix method and finite element method, the modified finite element-transfer matrix method and its algorithm for eigenvalue problems are presented. By using this method, the speedy computation of eigenvalue problem of flexible structures can be realized, and the repeated eignvalue problem can be solved simply and conveniently. This method has the low order of system matrix, high computational efficiency, and stability. Formulations of this method, as well as some numerical examples, are given to validate the method.

The rapid computation of random eigenvalue problems of uncertain structures is the key point in structural dynamics, and it is prerequisite to the efficient dynamic analysis and optimal design of structures. In this paper, by combining finite element-transfer matrix method (FE-TMM) with perturbation method, a new method named as perturbation FE-TMM is presented for random eigenvalue problems of uncertain structures. By using the proposed method, the rapid computation of random eigenvalue problems of uncertain structures with complicated shapes and boundaries can be achieved, and the repeated eignvalues and characteristic vectors can be solved conveniently. Compared with stochastic finite element method, this method has the low memory requirement, high computational efficiency and high computational stability. It has more advantages for dynamic design of uncertain structures. Formulations as well as some numerical examples are given to validate the method.

Introduction. Corporate governance, as a basis for ensuring the efficient use of corporate resources, can be built on a range of models that have both advantages and disadvantages. Neo-institutional theory, in particular its separate component is agency theory. It is one of the theories that allows to substantiate the reasons for the decline in the quality of implemented corporate governance systems and to formulate ways to improve it, in particular, taking into account the role of accounting in ensuring the effectiveness of their functioning.Purpose. The aim of the article is to monitor essence and peculiarities of manifestation of agency problem in corporate governance and substantiation of place of accounting in its solution.Methods. The range of research methods related to the solution of the agent problem in the corporate governance system is applied. Dialectical method of cognition and the systematic approach to the interpretation of corporate governance, the monographic method for monitoring the positions of scientists in the sphere of solving the agent problem, the abstract and logical method for theoretical generalizations and formulation conclusions are used in the research.Results. The necessity of accounting development in solving the agency problem in corporate management is substantiated. The peculiarities of the development of neo-institutional theory as a theoretical basis of corporate governance are revealed. The necessity to study agency theory as a means of solving problems in corporate governance is substantiated. The essence of agency problem in corporate structures is revealed and the causes of its occurrence are identified. The theoretical principles of agency problem in corporate structures are highlighted. Cases of manifestation of agency problem in corporate structures are analyzed. The basic directions of improvement of the accounting system of the corporate structure with the purpose of minimizing consequences of occurrence of agency problem are highlighted.Discussion. It is advisable to focus on optimizing specific elements of the corporate accounting system in further research in order to avoid agency issues in the corporate governance system.

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickness is small. In this paper we show an effective way of resolving this difficulty by invoking a special preconditioning technique associated with the effective dimensional reduction algorithm (EDRA). As an example, we present an algorithm for computing the minimal eigenvalue of a thin elastic plate and we show both theoretically and numerically that it is robust with respect to both the thickness and discretization parameters, i.e. the convergence does not deteriorate with diminishing thickness or mesh refinement. This robustness is sine qua non for the efficient computation of large-scale eigenvalue problems for thin elastic structures.

Parking Guidance and Information (PGI) signs are thought to enable a more efficient use of the available parking stock. Despite the installation of PGI systems in many cities and their operation for a number of years, there is a lack of reliable evidence of the size of the benefits that these systems can achieve. This paper describes the development of driver parking choice models (both during the journey and pre-trip) and the implementation of these models in the existing network traffic simulation model RGCONTRAM. Besides quantifying the effects of the PGI system on both the drivers seeking suitable parking spaces and the parking stock itself, this also enables quantification of the impact of parking choice on the wider network. Factors influencing PGI effectiveness are described and conclusions are drawn that illustrate the potential of PGI to induce the demand to spread more efficiently across the parking stock.