Contrasts in the basins of attraction of structurally identical iterative root finding methods

A numerical comparison is performed between three methods of third order with the same structure, namely BSC, Halley’s and Euler–Chebyshev’s methods. As the behavior of an iterative method applied to a nonlinear equation can be highly sensitive to the starting points, the numerical comparison is carried out, allowing for complex starting points and for complex roots, on the basins of attraction in the complex plane. Several examples of algebraic and transcendental equations are presented.

Radial Distortion Self-Calibration

In cameras with radial distortion, straight lines in space are in general mapped to curves in the image. Although epipolar geometry also gets distorted, there is a set of special epipolar lines that remain straight, namely those that go through the distortion center. By finding these straight epipolar lines in camera pairs we can obtain constraints on the distortion center(s) without any calibration object or plumbline assumptions in the scene. Although this holds for all radial distortion models we conceptually prove this idea using the division distortion model and the radial fundamental matrix which allow for a very simple closed form solution of the distortion center from two views (same distortion) or three views (different distortions). The non-iterative nature of our approach makes it immune to local minima and allows finding the distortion center also for cropped images or those where no good prior exists. Besides this, we give comprehensive relations between different undistortion models and discuss advantages and drawbacks.

The use of quantitative performance information by local elected politicians in top managers’ performance evaluation: case studies

This paper studies the use of results oriented performance information (outputs and outcomes) by local elected politicians (aldermen) in top managers’ performance evaluation. The main goal is to understand the top managers’ performance evaluation process conducted by Portuguese aldermen and to identify the dominant evaluation style. In line with Bogt (2001), an exploratory field research was developed in three large municipalities: Porto, Braga and Matosinhos. We intend to answer the following research questions: to what extent are local politicians (aldermen) 1 using results information (about outputs and outcomes) to evaluate top managers’ performance? Do aldermen give any importance to quantitative output information and report them on current planning and control documents? Will the output performance information be used on performance evaluation in a different way concerning policy field (task orientation)? Based on the Hopwood evaluation styles (adapted from the private to the public sector by Bogt, 2001), we have found that the performance evaluation process of top managers is more featured by the ‘operations-conscious styles’ (or ‘implicit style’). Portuguese aldermen recognize the importance to quantify outputs and outcomes, but these days they focus on the information about activities and the realized operations when they evaluate performance. We haven´t found significant differences between different tasks (some exceptions for culture and environment areas). However, the municipality of Matosinhos paid more attention on quantitative performance information. This finding is reinforced by the quality of quantitative data on outputs reported on its management report. Generally speaking, aldermen are aware that more attention should be paid to quantitative information about results and performance, taking into account recent reforms introduced in Portuguese municipalities (PLG) on this field, but the ‘implicit’ style is dominant.