Optimal design of efficient acoustic antenna arrays
Mathematical Programming: Series A and B
The accuracy of floating point summation
SIAM Journal on Scientific Computing
An example of error propagation reinterpreted as subtractive cancellation—revisited
ACM SIGNUM Newsletter
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The simple recursive algorithm Ik = 1 - k Ik-1 with I0 = 1 - 1/e (the result of an integration by parts) has served as an example of catastrophic error propagation. The traditional interpretation is that an initially small roundoff error in 1/e grows by a factor of k1. This note presents an alternate error analysis in terms of subtractive cancellation. From this perspective, the precise error is observable in detail, as is the effect of the floating point mantissa length. (Related material is referenced in 6.)