BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-89-12
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: Backward error assertions for checking solutions to systems
               of linear equations
        TYPE:: Manuscript
      AUTHOR:: Boley, Daniel L.
      AUTHOR:: Golub, Gene H.
      AUTHOR:: Makar, Samy R.
      AUTHOR:: Saxena, Nirmal R.
      AUTHOR:: McCluskey, Edward J.
        DATE:: November 1989
       PAGES:: 12
    ABSTRACT:: This paper presents an assertion scheme based on the backward
               error analysis for error detection in algorithms that solve a
               system of linear equations, Ax = b. This Backward Error
               Assertion Model can be easily instrumented in a Watchdog
               processor environment. The complexity of verifying assertions
               is O($n^2$) compared to the O($n^3$) complexity of algorithms
               solving Ax = b. Unlike other proposed error detection
               methods, this assertion model does not require any encoding
               of matrix A. Experimental results under various error models
               are presented to validate the effectiveness of these
               assertions.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-89-12