Statistical Optimization for Geometric Fitting: Theoretical Accuracy Bound and High Order Error Analysis

Stopping rules and backward error analysis for bound-constrained optimization

Termination criteria for the iterative solution of bound-constrained optimization problems are examined in the light of backward error analysis. It is shown that the problem of determining a suitable perturbation on the problem’s data corresponding to the definition of the backward error is analytically solvable under mild assumptions. Moreover, a link between existing termination criteria and ...

Error bound optimization using second order cone programming

In safety of life applications using satellite navigation, the Protection Level (PL) equation translates what is known about the pseudorange errors into a hard bound on the positioning error (the Protection Level). The current PL equations for Satellite Based Augmentation Systems are based on Gaussian statistics: all errors are characterized by a zero mean Gaussian distribution which is an uppe...

Novel Genetic Fitting Algorithms and Statistical Error Analysis Methods for X-ray Reflectivity Analysis

High Accuracy Ellipse-Specific Fitting

We propose a new method that always fits an ellipse to a point sequence extracted from images. The currently known best ellipse fitting method is hyper-renormalization of Kanatani et al., but it may return a hyperbola when the noise in the data is very large. Our proposed method returns an ellipse close to the point sequence by random sampling of data points. Doing simulation, we show that our ...

Approximation accuracy, gradient methods, and error bound for structured convex optimization

Convex optimization problems arising in applications, possibly as approximations of intractable problems, are often structured and large scale. When the data are noisy, it is of interest to bound the solution error relative to the (unknown) solution of the original noiseless problem. Related to this is an error bound for the linear convergence analysis of first-order gradient methods for solvin...