Methodology and analysis for comparing discrete linear l₁approximation codes

A Test Problem Generator for Discrete Linear L 1 Approximation Problems

“…. fl*m. In the context of evaluating Ll-approximation computer codes [8], however, it is also desirable to know whether or not this represents the only solution to the generated problem. As a matter of fact, the problems generated by the procedure described here will always possess a unique solution if X is of full column rank m.…”

“…This paper describes the development and implementation of a generation procedure having a number of desirable features that permit the user to specify and vary the data structures to be tested. T h e procedure incorporates m a n y of the characteristics suggested by Holland [9] as useful in testing robustness of regression programs and has been used in a recent comparison of L~-approximation codes [8]. It also can produce, as a special case, data structures similar to those obtained through the L1 generator of Kennedy, Gentle, and Sposito [10].…”

Generators for discrete polynomial L1 approximation problems

“…Polynomial approximation proble ms are freque ntly e ncountered in practice (e.g., amo ng our hand-picked problems), and also enjoy an extensive theoreti cal basis [7 , 18,23]. Moreover, such proble ms are known to admit a range of "ill-conditioning" and nume ri cal difficulties [10], notably evidenced in our previous testing efforts using 27 hand-pic ked proble ms [13] and in recent results obtained using the first of these two generators [8].…”

Statistical Analysis of Computational Tests of Algorithms and Heuristics

“…Some are examples of linear regression analysis. [16,21,42] Two examples implement experimental design and analysis of variance techniques. [4,5] Other methodological studies discuss visualization, [52] exploratory data analysis, [29,65] and distribution-free hypothesis tests, and estimation of optimal values based on heuristic solutions.…”