1. Error Analysis in Floating-Point Arithmetic;Carr;Comm. ACM,1959
2. Computable Error Bounds for Direct Solution of Linear Equations;Chartres;J. ACM,1967
3. This provides an a postiori analysis of direct solution methods for simultaneous linear equations corresponding to Wilkinson's a priori analysis and includes some normalized floating-point arithmetic considerations and the use of extended precision for intermediate results. Applicable methods are Gaussian elimination with pivot search and triangular factorization.
4. Hammer, C., Statistical Validation of Mathematical Computer Routines, Proc. Spring Joint Comput. Conf. pp. 331–333(1967).
5. A Monte Carlo-like test scheme for mathematical subroutines of particular kinds, which assumes uniform distribution of rounding errors, and says “precision” where most workers say “accuracy” (to denote number of valid digits in a number). To solve a transcendental expression for error bounds, this author uses an approximation evaluated at a large number of randomly selected argument values within the range over which each function is to be tested.