On the convergence of iterative voting: how restrictive should restricted dynamics be?

We study convergence properties of iterative voting procedures. Such procedures are defined by a voting rule and a (restricted) iterative process, where at each step one agent can modify his vote towards a better outcome for himself. It is already known that if the iteration dynamics (the manner in which voters are allowed to modify their votes) are unrestricted, then the voting process may not converge. For most common voting rules this may be observed even under the best response dynamics limitation. It is therefore important to investigate whether and which natural restrictions on the dynamics of iterative voting procedures can guarantee convergence. To this end, we provide two general conditions on the dynamics based on iterative myopic improvements, each of which is sufficient for convergence. We then identify several classes of voting rules (including Positional Scoring Rules, Maximin, Copeland and Bucklin), along with their corresponding iterative processes, for which at least one of these conditions hold

Iterative procedures for identification of nonlinear interconnected systems

This work addresses the identification problem of a discrete-time nonlinear system composed by linear and nonlinear subsystems. Systems in this class will be represented by Linear Fractional Transformations. Iterative identification procedures are examined, that alternate between the estimation of the linear and the nonlinear components. The burden of identification falls naturally on the nonlinear subsystem, as techniques for identification of linear systems have long been established. Two approaches are examined. A point-wise identification of the nonlinearity, recently proposed in the literature, is applied and its advantages and drawbacks are outlined. An alternative procedure that employs piecewise affine approximation techniques is proposed. Numerical examples demonstrate the efficiency of the proposed algorithm

On the Absence of Spurious Eigenstates in an Iterative Algorithm Proposed By Waxman

We discuss a remarkable property of an iterative algorithm for eigenvalue problems recently advanced by Waxman that constitutes a clear advantage over other iterative procedures. In quantum mechanics, as well as in other fields, it is often necessary to deal with operators exhibiting both a continuum and a discrete spectrum. For this kind of operators, the problem of identifying spurious eigenpairs which appear in iterative algorithms like the Lanczos algorithm does not occur in the algorithm proposed by Waxman

Exact Real Arithmetic with Perturbation Analysis and Proof of Correctness

In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to guarantee the correctness of the approximations. Moreover, we develop and apply a perturbation analysis method to show that our approximation procedures only recompute expressions when unavoidable. In the last decade, various theories have been developed and implemented to realize real computations with arbitrary precision. Proof of correctness for existing approaches typically consider basic algebraic operations, whereas detailed arguments about transcendental operations are not available. Another important observation is that in each approach some expressions might require iterative computations to guarantee the desired precision. However, no formal reasoning is provided to prove that such iterative calculations are essential in the approximation procedures. In our approximations of real functions, we explicitly relate the precision of the inputs to the guaranteed precision of the output, provide full proofs and a precise analysis of the necessity of iterations

Iterative procedures for space shuttle main engine performance models

Performance models of the Space Shuttle Main Engine (SSME) contain iterative strategies for determining approximate solutions to nonlinear equations reflecting fundamental mass, energy, and pressure balances within engine flow systems. Both univariate and multivariate Newton-Raphson algorithms are employed in the current version of the engine Test Information Program (TIP). Computational efficiency and reliability of these procedures is examined. A modified trust region form of the multivariate Newton-Raphson method is implemented and shown to be superior for off nominal engine performance predictions. A heuristic form of Broyden's Rank One method is also tested and favorable results based on this algorithm are presented

Study of optimum discrete estimators in measurement analysis

Study of statistical techniques for obtaining estimates of true data parameters uses discrete measured quantities containing random error. These techniques develop estimation procedures as an iterative algorithm for digital computation in real time

Redressing the Silent Interim: Precautionary Action & Short Term Tests in Toxicological Risk Assessment

The author recommends that a stronger emphasis be placed on creating and implementing short-term tests that use iterative, conservative-based, tiered procedures in conjunction with a precautionary attitude during the interim phase of toxicological risk assessments