UC Research Repository Community:
http://hdl.handle.net/10092/1
2015-07-30T00:16:50ZAccelerations for global optimization methods that use second derivative information
http://hdl.handle.net/10092/10710
Title: Accelerations for global optimization methods that use second derivative information
Authors: Baritompa, William P.; Cutler, Adele
Abstract: Two new improvements for the algorithm of Breiman & Cutler are presented. Better envelopes can be built up using positive definite quadratic forms. Better utilization of first and second derivative information is attained by combining both global aspects of curvature and local aspects nearthe global optimum. The basis of the results is the geometric viewpoint developed by the first author and can be applied to a number of covering type methods. Improvements in convergence rates are demonstrated empirically on standard test functions.1993-01-01T00:00:00ZA projected Lagrangian algorithm for semi-infinite programming
http://hdl.handle.net/10092/10709
Title: A projected Lagrangian algorithm for semi-infinite programming
Authors: Coope, Ian D.; Watson, G. A.
Abstract: A globally convergent algorithm is presented for the solution of a wide class of semi-infinite programming problems. The method is based on the solution of a sequence of equality constrained quadratic programming problems, and usually has a second order convergence rate. Numerical results illustrating the effectiveness of the method are given.1983-01-01T00:00:00ZEye tracking and studying examples: how novices and advanced learners study SQL examples
http://hdl.handle.net/10092/10706
Title: Eye tracking and studying examples: how novices and advanced learners study SQL examples
Authors: Shareghi Najar, A.; Mitrovic, A.; Neshatian, K.
Abstract: Eye tracking provides information about a user’s eye gaze movements. For many years, eye tracking has been used in Human Computer Interaction (HCI) research. Similarly, research on computerised educational systems also relies heavily on students’ interactions with systems, and therefore eye tracking has been used to study and improve learning. We have recently conducted several studies on using worked examples in addition to scaffolded problem solving. The goal of the project reported in this paper was to investigate how novices and advanced students learn from examples. The study was performed in the context of SQL-Tutor, a mature Intelligent Tutoring System (ITS) that teaches SQL. We propose a new technique to analyse eye-gaze patterns named EGPA. In order to comprehend an SQL example, students require the information about tables’ names and their attributes which are available in a database schema. Thus, if students paid attention to the database schema, they would understand SQL examples more easily. We analysed students’ eye movement data from different perspectives, and found that advanced students paid more attention to database schema than novices. In future work, we will use the findings from this study to provide proactive feedback or individualised amounts of information.2015-01-01T00:00:00ZUniform approximation from Tchebycheff systems
http://hdl.handle.net/10092/10705
Title: Uniform approximation from Tchebycheff systems
Authors: Brookes, Richard Gordon
Abstract: This report is concerned with the study of best uniform approximation
to f E C[a,b) from the linear space generated by some finite subset
U == {uo,u1, ... ,u} of C[a,b).
n
p* E span U such that
By a best uniform approximation we mean
max{jf(x) ~p*(x) j: x E [a,b]} = min{max{jf(x) -p(x) I x E [a,b]}
: p E span u}.
We explore, firstly, the case U = {l,x, ... ,xn}. It will be shown in
Section 4 that in this situation each f E C[a,b) has a unique best approximation
and for this best approximation there is a strong characterisation
theorem. It is then natural to ask whether these results are true for a
more general U = {u 0 ,u 1 , ••• ,u } .
n
If a strong type of linear independence
known as the Haar condition is imposed on U then this will indeed turn out
1.
to be the case. We will attempt to develop this condition using an approach
more intuitively obvious than those found in many standard texts.
When the Haar condition is not satisfied the problem rapidly becomes
complicated and it appears that much work remains to be done in this area.
A theorem concerning a particularly simple situation is given in Section 8.1987-01-01T00:00:00Z