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A Floating-Point Trick to Solve Boundary-Value Problems Faster: Scientific Computing and Matrix Computations Seminar

Seminar: Departmental | March 20 | 12:10-1 p.m. | 380 Soda Hall

W. Kahan, UC Berkeley

Electrical Engineering and Computer Sciences (EECS)

This talk resuscitates an old trick to accelerate the numerical solution of certain discretized boundaryvalue problems.
Without the trick, half the digits carried by the arithmetic can be lost to roundoff when
the discretization’s grid-gaps get very small. The trick can obtain adequate accuracy from arithmetic with
float variables 4-bytes wide instead of double variables 8-bytes wide. Wider data moves slower through
the computer’s memory system and pipelines. The trick is tricky for programs written in MATLAB™ 7,
JAVA, FORTRAN and post-1985 ANSI C. The trick is easy for the original Kernighan-Ritchie C of the
late 1970s, and for a few implementations of C99 that fully support IEEE Standard 754 for Binary
Floating-Point., 510-516-4321