The statistical theory of relative errors in floating-point computation /

Thesis (M. S.)--University of Illinois at Urbana-Champaign.

A priori prediction of roundoff error accumulation in the solution of a super-large geodetic normal equation system /

"June 1980."

Methods for automatic error analysis of numerical algorithms /

Vita.

Solving triangular systems on a parallel computer /

Includes bibliographical references.

Gaussian elimination and numerical instability /

"UILU-ENG 77 1714."

An error analysis of solutions to sparse linear programming problems,

"Supported in part by the Advanced Research Projects Agency ... contract no. US AF 30(602) 4144."

QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

Sequential decision fusion for controlled detection errors

Information fusion in biometrics has received considerable attention. The architecture proposed here is based on the sequential integration of multi-instance and multi-sample fusion schemes. This method is analytically shown to improve the performance and allow a controlled trade-off between false alarms and false rejects when the classifier decisions are statistically independent. Equations developed for detection error rates are experimentally evaluated by considering the proposed architecture for text dependent speaker verification using HMM based digit dependent speaker models. The tuning of parameters, n classifiers and m attempts/samples, is investigated and the resultant detection error trade-off performance is evaluated on individual digits. Results show that performance improvement can be achieved even for weaker classifiers (FRR-19.6%, FAR-16.7%). The architectures investigated apply to speaker verification from spoken digit strings such as credit card numbers in telephone or VOIP or internet based applications.

To err (on the road) is human? An on-road study of driver errors

Human error, its causes and consequences, and the ways in which it can be prevented, remain of great interest to road safety practitioners. This paper presents the findings derived from an on-road study of driver errors in which 25 participants drove a pre-determined route using MUARC's On-Road Test Vehicle (ORTeV). In-vehicle observers recorded the different errors made, and a range of other data was collected, including driver verbal protocols, forward, cockpit and driver video, and vehicle data (speed, braking, steering wheel angle, lane tracking etc). Participants also completed a post trial cognitive task analysis interview. The drivers tested made a range of different errors, with speeding violations, both intentional and unintentional, being the most common. Further more detailed analysis of a sub-set of specific error types indicates that driver errors have various causes, including failures in the wider road 'system' such as poor roadway design, infrastructure failures and unclear road rules. In closing, a range of potential error prevention strategies, including intelligent speed adaptation and road infrastructure design, are discussed.

Modeling object identification and tracking errors on image-based safety assessment of earthmoving operations

Object identification and tracking have become critical for automated on-site construction safety assessment. The primary objective of this paper is to present the development of a testbed to analyze the impact of object identification and tracking errors caused by data collection devices and algorithms used for safety assessment. The testbed models workspaces for earthmoving operations and simulates safety-related violations, including speed limit violations, access violations to dangerous areas, and close proximity violations between heavy machinery. Three different cases were analyzed based on actual earthmoving operations conducted at a limestone quarry. Using the testbed, the impacts of device and algorithm errors were investigated for safety planning purposes.

Chronological age and age-related cognitive deficits are associated with an increase in multiple types of driving errors in late life

Objective: Older driver research has mostly focused on identifying that small proportion of older drivers who are unsafe. Little is known about how normal cognitive changes in aging affect driving in the wider population of adults who drive regularly. We evaluated the association of cognitive function and age, with driving errors. Method: A sample of 266 drivers aged 70 to 88 years were assessed on abilities that decline in normal aging (visual attention, processing speed, inhibition, reaction time, task switching) and the UFOV® which is a validated screening instrument for older drivers. Participants completed an on-road driving test. Generalized linear models were used to estimate the associations of cognitive factor with specific driving errors and number of errors in self-directed and instructor navigated conditions. Results: All errors types increased with chronological age. Reaction time was not associated with driving errors in multivariate analyses. A cognitive factor measuring Speeded Selective Attention and Switching was uniquely associated with the most errors types. The UFOV predicted blindspot errors and errors on dual carriageways. After adjusting for age, education and gender the cognitive factors explained 7% of variance in the total number of errors in the instructor navigated condition and 4% of variance in the self-navigated condition. Conclusion: We conclude that among older drivers errors increase with age and are associated with speeded selective attention particularly when that requires attending to the stimuli in the periphery of the visual field, task switching, errors inhibiting responses and visual discrimination. These abilities should be the target of cognitive training.

Third-order theory of spectacle lenses applied to correction of peripheral refractive errors

Purpose: To demonstrate that relatively simple third-order theory can provide a framework which shows how peripheral refraction can be manipulated by altering the forms of spectacle lenses. Method: Third-order equations were used to yield lens forms that correct peripheral power errors, either for the lenses alone or in combination with typical peripheral refractions of myopic eyes. These results were compared with those of finite ray-tracing. Results: The approximate forms of spherical and conicoidal lenses provided by third-order theory were flatter over a moderate myopic range than the forms obtained by rigorous raytracing. Lenses designed to correct peripheral refractive errors produced large errors when used with foveal vision and a rotating eye. Correcting astigmatism tended to give large errors in mean oblique error and vice versa. When only spherical lens forms are used, correction of the relative hypermetropic peripheral refractions of myopic eyes which are observed experimentally, or the provision of relative myopic peripheral refractions in such eyes, seems impossible in the majority of cases. Conclusion: The third-order spectacle lens design approach can readily be used to show trends in peripheral refraction.