Faculty Publications (Engineering)
http://hdl.handle.net/1828/1424
This collection contains full text research publications authored or co-authored by University of Victoria researchers.2020-01-26T12:53:37ZComputing L1 Straight-Line Fits to Data
http://hdl.handle.net/1828/11501
Computing L1 Straight-Line Fits to Data
Barrodale, I
In 1971 Frank D.K. Roberts and I developed the BR algorithm ([i],[ii]), complete with Fortran code [iii], for calculating L1 solutions to overdetermined systems of m linear equations in n unknown parameters2. The challenge here is to develop fast code for L1 fitting by straight lines (n = 2) to big data sets (m ≥ 106) that largely avoids the frustration of sluggish run times.
2020-01-23T00:00:00ZBest Rational Approximation and Strict Quasi-Convexity
http://hdl.handle.net/1828/11492
Best Rational Approximation and Strict Quasi-Convexity
Barrodale, I
If a continuous function is strictly quasi-convex on a convex set $\Gamma $, then every local minimum of the function must be a global minimum. Furthermore, every local maximum of the function on the interior of $\Gamma $ must also be a global minimum. Here, we prove that any minimax rational approximation problem defines a strictly quasi-convex function with the property that a best approximation (if one exists) is a minimum of that function. The same result is not true in general for best rational approximation in other norms.
1971-01-01T00:00:00ZAn Improved Algorithm for Discrete L1 Linear Approximation
http://hdl.handle.net/1828/11491
An Improved Algorithm for Discrete L1 Linear Approximation
Barrodale, I; Roberts, F.D.K.
By modifying the simplex method of linear programming, we are able to present an algorithm for $l_1 $-approximation which appears to, be superior computationally to any other known algorithm for this problem.
1972-01-01T00:00:00ZComputing L1 Straight-Line Fits to Data (Part 1)
http://hdl.handle.net/1828/11460
Computing L1 Straight-Line Fits to Data (Part 1)
Barrodale, I
This report outlines improvements to an old algorithm for fitting L1 straight lines to data. The improvements are designed to accommodate L1 line fitting to much larger data sets than previously practical. The algorithmic details are provided in a form suitable for students and others to implement in any programming language of their choice.
2020-01-04T00:00:00Z