Parallelism and Error Reduction in a High Performance Environment

Acknowledgements I want to thank my advisor, Dr. R. Clint Whaley, for an enormous amount of work on my behalf, and for his excellent academic advice. I want to thank my wife for her support and enthusiasm for my academic pursuits. The following two paragraphs are required text by UTSA: " This Masters Thesis/Recital Document or Doctoral Dissertation was produced in accordance with guidelines which permit the inclusion as part of the Masters The-sis/Recital Document or Doctoral Dissertation the text of an original paper, or papers, submitted for publication. The Masters Thesis/Recital Document or Doctoral Dis-sertation must still conform to all other requirements explained in the Guide for the Preparation of a Masters Thesis/Recital Document or Doctoral Dissertation at The University of Texas at San Antonio. It must include a comprehensive abstract, a full introduction and literature review, and a final overall conclusion. Additional material (procedural and design data as well as descriptions of equipment) must be provided in sufficient detail to allow a clear and precise judgment to be made of the importance and originality of the research reported. It is acceptable for this Masters Thesis/Recital Document or Doctoral Dissertation to include as chapters authentic copies of papers already published, provided these meet type size, margin, and legibility requirements. In such cases, connecting texts, which provide logical bridges between different manuscripts, are mandatory. Where the student is not the sole author of a manuscript, the student is required to make an explicit statement in the introductory material to that manuscript describing the students contribution to the work and acknowledging the contribution of the other author(s). The signatures of the Supervising Committee which precede all other material in the Mas-This dissertation details contributions made by the author to the field of computer science while working to improve the performance of a state-of-the-art linear algebra library intended for use on commodity platforms. These platforms and libraries have become a de facto standard for most scientific researchers. There are three significant contributions to the field. The superblock family of summation algorithms generalizes the dot product and its error analysis, and allows floating point error to be controlled with a desired target bound and performance loss and with workspace determined at compile time. It demonstrates empirically that theoretical error bounds are good predictors of actual errors. The opposite had been asserted by leading experts in the field. The Master Last algorithm identifies and …