Local and Semi-Local Convergence

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Convergence of Halley’s method for operators with the bounded second Fréchet derivative in Banach spaces

Convergence of Halley’s method for operators with the bounded second Fréchet derivative in Banach spaces

In this paper, we present a semi-local convergence analysis of Halley’s method for approximating a locally unique solution of a nonlinear equation in a Banach space setting, where we assume that the second Fréchet-derivative is bounded. Numerical examples are used to show that the new convergence criteria can provide better information than those provided by the convergence criteria developed earlier. MSC: 65G99; 65J15; 65H10; 47H17; 49M15

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On iterative computation of fixed points and optimization

On iterative computation of fixed points and optimization

The rest of the study is organized as follows: Section  contains the notions of general- ized Lipschitz conditions and the majorizing sequences for the method (GNA). In order for us to make the paper as self-contained as possible, the notion of quasi-regularity is re-introduced (see, for example, []) in Section . Semi-local convergence analysis of the method (GNA) using L-average conditions is presented in Section . In Section , some convex majorant conditions are used for the semi-local convergence of the method (GNA). 2 Generalized Lipschitz conditions and majorizing sequences

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Search | Preprints

Search | Preprints

sequence call it { t ¯ n } is even tighter than {t n }. Hence, we have extended the applicability of method (??) in the semi-local convergence analysis too. These improvements are derived under the same conditions as in [?], since the com- putation of L is included in the computation of K as a special case. Examples where the new constants are smaller than the older ones can be found in the numerical section that follows and in [?, ?, ?,?, ?].

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Health status convergence at the local level: empirical evidence from Austria

Health status convergence at the local level: empirical evidence from Austria

Regarding sigma-convergence, we find rather mixed results. While the weighted standard deviation indicates an increase in equality for all four variables, the picture appears less clear when correcting for the decreasing mean in the distribution (coefficient of variation and Theil-index of inequality). On the contrary, we find highly significant coefficients for absolute and condi- tional beta-convergence between the periods. The highly significant beta-convergence across communities might be caused by (i) the efforts to harmonize and centralize the health policy at the federal level in Austria since the 1970s, (ii) the diminishing returns of the input factors in the health production function, which might lead to convergence, as the general conditions (e.g. income, education etc.) improve over time, and (iii) the mobility of people across regions, as people tend to move to regions/communities which exhibit more favorable liv- ing conditions. While these results are confirmed by several robustness tests, we also find evidence for the existence of convergence clubs. Both the significance of the dummy variables for genetic structures in our condi- tional beta-convergence estimation as well as the con- siderable difference of the beta-coefficients when running separate regressions for these regions can be interpreted as evidence for possible convergence clubs. In order to test for differences in the beta-coefficients within the distribution we also ran quantile regressions for the lower and upper quartile of the distribution. Once again, the impression of divergences in the coeffi- cients in different parts of the distribution was con- firmed, albeit the conclusion of beta-convergence across communities is unaffected by this result. Our results basically confirm the findings from [5] for Canada and [37] for India, while the studies by [35] and [36] find a significant Matthew effect for Canada and the US in recent decades.

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A Semi Harmonic Frequency Pattern Organizes Local and Non Local States by Quantum Entanglement in both EPR Studies and Life Systems

A Semi Harmonic Frequency Pattern Organizes Local and Non Local States by Quantum Entanglement in both EPR Studies and Life Systems

John Bell in theory proved that the supposed non-local effect of quan- tum-entangled particles was probably real, and this became known as Bell’s theorem or inequality. He resolved the paradox by pointing to a failure of local realism itself and proved the impossibility of completing quantum mechanics with local hidden variable theories [8]. Bell’s theorem ruled out local hidden va- riables as a viable explanation of quantum mechanics, and it left the door open for non-local hidden variables. Bell concluded: in a theory in which parameters are added to quantum mechanics to determine the results of individual mea- surements, without changing the statistical predictions, there must be a mechan- ism whereby the setting of one measuring device can influence the reading of another instrument, however remote. So, the signal involved must propagate in- stantaneously. Numerous experiments agree now with the predictions of this quantum mechanical theory, and show that differences between correlations that cannot be explained by local hidden variables. Thus the experimental results

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Convergence Model of Governance: A Case Study of the Local Government System of Pakistan

Convergence Model of Governance: A Case Study of the Local Government System of Pakistan

The future of devolution plan in Pakistan may be analysed in view of our Convergence model. This model views stability of the local Govt. system drawn on Devolution Plan 2001. It claims that as there would be more volatile and non-committed (floating) number of agents in the political market and governance system, there is more probability of divergence; i.e. the system will remain unstable. Contrary to that more is the systematic trend in political market and governance system more is the probability that the convergence in the system occurs and that in turn leads to stability of the over all system. In this ‘Convergence’ Model different types of agents have been highlighted on the basis of their political affiliation and being in competition as ruling elite and/or their allies and non-ruling elite and/or their allies.

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Local texture convergence within three communities in Fiordland, New Zealand

Local texture convergence within three communities in Fiordland, New Zealand

There have been only a few studies of texture convergence using an explicit null model that allows significance to be calculated. Those studies have generally compared sites remote from each other, allowing some evaluation of evolutionary processes (e.g. Schluter, 1986; Wiens, 1991), but none of these has examined within-community convergence, the level at which, we argue, convergence due to ecological sorting can best be seen. We examined variation within three communities, to make such a test. The hypothesis we test is that patches of a community will be more similar in texture than expected under a null model. Our null model is that within each site species co-occur without any constraint caused by their characters. Almost all answers in ecology are dependent on the spatial sampling scale (i.e. spatial grain) at which they are investigated (Wiens, 1989b). We examine texture convergence at a range of spatial scales, for the first time.

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Convergence analysis of a residual local projection method for the Navier-Stokes equation

Convergence analysis of a residual local projection method for the Navier-Stokes equation

The stability and convergence analysis of the RELP method is based on the fixed point theory presented in [8, 17] and used in [24] to analyze the SDFEM method originally proposed in [13] in the case where diffusion dominates and in [10] for a pressure-stabilized finite element method. Here, we extend that idea and prove that the original RELP method is well-posed and achieve optimal convergence in natural norms. Due to the particular structure of the method, the proof requests the construc- tion of a new stabilized finite element method for the Stokes equation, related to the one given in [1], which is also analyzed. Finally, we establish that the postprocessed divergence-free velocity field is also optimally convergent.

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Local Governance and Local Knowledge

Local Governance and Local Knowledge

great significance in the political, economic, cultural and social life [9]. From a political point of view, the protection of cultural diversity is the key to ensuring national stability, and it is also the responsibility of all levels of local govern- ment. From an economic point of view, the unique culture within the region can bring some economic benefits to the local [10]. For example, local governments can develop tourism to promote local economic growth and improve people’s living standards according to local natural or human conditions. So local know- ledge can help local government to find the right direction of development. From a legal point of view, the native soil society has its own set of knowledge about crime and punishment and the solution to the dispute and it provides guidance for local governments to resolve disputes in the jurisdiction [11]. Local governments can resolve disputes through a combination of local remedies within the limits permitted by law.

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Local polynomial estimations of time varying coefficients for local stationary diffusion models

Local polynomial estimations of time varying coefficients for local stationary diffusion models

The theory of local stationary process is introduced by Dahlhaus [, ]. Intuitively speak- ing, a process is locally stationary if the process behaves like a stationary diffusion process in a neighborhood of a chosen time point. In recent years, various efforts have been made to explicitly express the local stationary models. For example, Koo and Linton [] discuss semi-parametric estimations of a class of locally stationary diffusion processes with lo- cally linear drift. Vogt [] considers nonparametric regression for a locally stationary time series model. To the best of our knowledge, few literature works have researched local polynomial estimations in locally stationary time-inhomogeneous diffusion models. This motivates us to consider the local estimations of the time-varying coefficients for locally stationary diffusion models.

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Studies on the effects of parameters on the convergence of local radial point interpolation method (LRPIM)

Studies on the effects of parameters on the convergence of local radial point interpolation method (LRPIM)

Recently Meshless method has attracted more attention from researchers and it is regarded as a potential numerical method in computational mechanics. Several meshless methods, such as smooth particle hydrodynamics (SPH) method [4-6], element free Galerkin (EFG) method [7], meshless local Petrov-Galerkin (MLPG) method [8-9], the point interpolation methods (PIM)[10-11] and local radial point interpolation method (LRPIM) proposed by Liu et al. [11]. In LRPIM, the point interpolation developed by the radial function basis is used to construct shape functions with delta function property. The widely used radial basis functions (RBFs) are multi-quadric (MQ), Gaussian (EXP) [12] and thin plate spline (TPS) function [13]. In this paper, the local weak forms are developed using weighted residual method locally from the partial differential equation of elastostatic linear 2D solids. We discus the effects of some parameters for radial basis function, and also the effects of size parameter of support and quadrature domains on the performance of the local radial point interpolation method LRPIM. Numerical results are presented to describe the convergence and accuracy, validity and efficiency of the present methods.

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Local Warming, Local Economic Growth, and Local Change in Democratic Culture

Local Warming, Local Economic Growth, and Local Change in Democratic Culture

Owing to global warming, winter and summer demands will both decrease towards higher latitudes. This softening climate produces pushes and pulls away from challenges, self- expression goals, individualism, and democracy in rich regions (e.g., Table 3, Sweden, no. 4; New Zealand, no. 7; Canada, nos. 6, 12), but away from threats, survival stress, collectivism, and autocracy in poor regions (e.g., Russia, nos. 118, 114, 100, 85). As winters hit harder than summers, combinations of less demanding winters and more demanding summers will strengthen rather than weaken democratic culture (e.g., Northwest China, no. 129; Kazakhstan, no. 116; Zambia, no. 108; Iran, no. 105), unless this tendency is counteracted by economic decline (e.g., Tajikistan, no. 26; Kyrgyzstan, no. 27). Global warming hits environmental livability hardest in poor tropical areas where both winter and summer demands increase. As a result, in Brazil Amazon (no. 38), Mali (no. 76), Burkina Faso (no. 79), Congo-Kinshassa (no. 90), and the like, local warming will strengthen rather than weaken threats, survival stress, collectivism, and autocracy. Only stronger economic growth, as evidenced by the case of Sudan (no. 135), can prevent this misery from being perpetuated.

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Study on Stability Convergence Rate of Chemostat Model of a Kind of Organism

Study on Stability Convergence Rate of Chemostat Model of a Kind of Organism

In this paper, the convergence rate of the local stability of a type of organic chemostat model (5) is studied.Firstly, the stability of model (5) is studied by using the stability geometric switching method,compared with the previous method of constructing central manifolds and using norm, namely Lyapunov function method, the method used in this paper is simpler.Therefore, the idea of stability geometric switching has great advantages in the study of local stability of time-delay dynamical systems.Secondly, the  -stability of model (5) is studied by using the time-delay dynamical system stability geometric switching method, that is, by introducing the factor  and controlling its size, the goal of fast convergence can be achieved.At last, the scientific nature of the theory is verified by numerical simulation with mathematical software on the basis of theoretical analysis.

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A smoothing and regularization predictor corrector method for nonlinear inequalities

A smoothing and regularization predictor corrector method for nonlinear inequalities

In this paper, we present a new smoothing and regularization predictor-corrector algo- rithm to solve the nonlinear inequalities, the global and local convergence are obtained. Furthermore, the smoothing parameter μ and the regularization parameter ε in our algo- rithm are viewed as independent variables. Preliminary numerical results show the effi- ciency of the algorithm.

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Convergence In State And Local Spending On Education:  Are Lotteries Ear Marked For Education The Key?

Convergence In State And Local Spending On Education: Are Lotteries Ear Marked For Education The Key?

Chart 1 gives a more analytical presentation of the data which will more formally indicate if the convergence hypothesis is credible. Chart 1 plots the relative (to the U.S. average) growth in per capita education spending for the 50 states with the relative (again to the U.S. average) 1977 spending. If convergence was indeed happening, one should see a negative relationship between the initial value of spending and the growth of spending. Chart 1 reveals such a relationship. The correlation between initial spending and growth was -0.68. A simple regression represented by the trend line in Chart 1 revealed that the negative slope is significantly less than zero.

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Diversity, local knowledge and use of stingless bees (Apidae: Meliponini) in the municipality of Nocupétaro, Michoacan, Mexico

Diversity, local knowledge and use of stingless bees (Apidae: Meliponini) in the municipality of Nocupétaro, Michoacan, Mexico

Bees are among the main pollinators of flowering plants throughout the world and their conservation is a current main issue of both science and society. This is a general premise for all bees ’ species but it acquires particular rele- vance for those species that in addition to pollination rep- resent provision ecosystem services as are several species of Meliponini. Nonetheless local experts of Nocupétaro perceive and recognize that extraction rates of bee pro- ducts have decreased more recently alongside the increase of vegetation clearing and use of insecticides threatening the permanence of stingless bees, local knowledge and the use of resources they provide persist in the study area. For this, it is relevant to establish the consequences that en- vironmental problems may have for both, populations of stingless bees and local culture associated with them. In this sense ethnozoological and ethnoentomolgical studies are a key reference to direct these efforts.

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Local solidarity

Local solidarity

Does this mean we have reached a place of no alternatives? I don’t believe so and I think there are examples, though far and few in between, of people who have achieved a good quality of life without a fanatic drive towards ‘growth’ that legitimizes the exploitation of the planet and its poor. There are examples of the creation of local and sustainable economies, both historical and contemporary. From the first recorded rebellion in Indian history by people against the rulers in their fight for access to commons in the 1500s, to the Indian independence struggle, to the present day anti- globalization protest movements, common people have fought for and will continue to fight for their rights over their ‘commons’. Most of these protests were and continue to be extra legal hidden forms of resistance and individual acts of violation resting on the support of a network. Apart from protests, a number of local self-help groups outside of the government and development institutions began to take active roles in changing people’s lives, restoring their spaces and changing their worlds. Mann (1986) suggests that such interstitial emergence is an important pathway of social change. Efforts include conservation of natural resources, reforestation, alternate local governing bodies, resort to local wisdom, and women’s participation in these initiatives. Most of the protests come from the Ecosystem people who face the danger of becoming Ecological Refugees. Fortunately, though Indian democracy is flawed, it is functioning, nobody is completely powerless and there are always avenues for expression of popular protest, even for the most disadvantaged.

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International convergence and local divergence

International convergence and local divergence

Since we want to reproduce some stylized facts, it is convenient for us to rule out any price-index e¤ect threatening to abort north-south convergence. Then, the relative-size e¤ect will remain as the single driving force. Therefore, > 1=2 appears as a natural fact for a north-south structure that (together with ! 1 ) could be enough to achieve international convergence in per-capita income. But let’s provide …rst a su¢cient condition for > 1=2 in terms of the parameters.

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Microloop prevention by introducting a local convergence delay

Microloop prevention by introducting a local convergence delay

This mechanism permit to solve all the transient forwarding loop in a network at the price of introducing complexity in the convergence process that may require strong monitoring by the service provider. Our solution reuses the OFIB concept but limits it to the first hop that experience the topology change. As demonstrated, our proposal permits to solve all the local transient forwarding loops that

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Local convergence of random graph colorings

Local convergence of random graph colorings

The single most tantalising feature of the random graph coloring problem is the interplay between local and global effects. Locally around almost any vertex the random graph is bipartite w.h.p. In fact, for any fixed average degree d > 0 and for any fixed ω the depth-ω neighborhood of all but o(n) vertices is just a tree w.h.p. Yet globally the chromatic number of the random graph may be large. Indeed, for any number k ≥ 3 of colors there exists a sharp threshold sequence d k-col = d k-col (n) such that for any fixed ε > 0,

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