Comments on the Reliability of Lawson and Hanson's Linear Distance Programming Algorithm: Subroutine LDP

TL;DR

This paper evaluates the reliability of the Lawson and Hanson Linear Distance Program by proposing test case generation strategies, providing problematic examples, and recommending output validation for improved robustness.

Contribution

It introduces a systematic approach for testing LDP software, presents concrete problematic cases, and advocates for output self-consistency checks as standard practice.

Findings

Generated test cases reveal issues in Lawson and Hanson's LDP module.

Three numerical examples demonstrate potential problems in the implementation.

Recommends output validation to ensure correctness with minimal overhead.

Abstract

This brief paper: (1) Discusses strategies to generate random test cases that can be used to extensively test any Linear Distance Program (LDP) software. (2) Gives three numerical examples of input cases generated by this strategy that cause problems in the Lawson and Hanson LDP module. (3) Proposes, as a standard matter of acceptable implementation procedures, that (unless it is done internally in the software itself, but, in general, this seems to be much rarer than one would expect) all users should test the returned output from any LDP module for self-consistency since it incurs only a small amount of added computational overhead and it is not hard to do.