Floating-Point Tricks to Solve Boundary-Value Problems
                        Faster

W. Kahan,  Prof. Emeritus
Math. Dept.,  and  E.E. & Computer Sci. Dept.,
University of California @ Berkeley

For  UCB's
Scientific & Engineering Numerical Computing Seminar
11 Sept. 2013

Abstract:  Some old tricks are resuscitated to accelerate
the numerical solution of certain discretized boundary-value
problems.  Without the tricks,  half the digits carried by
the arithmetic can be lost to roundoff when the
discretization's grid-gaps get very small.  The tricks can
procure adequate accuracy from arithmetic with  "float"
variables  4-bytes wide  instead of  "double"  variables
8-bytes wide that move slower through the computer's memory
system and pipelines.  Tricks are tricky for programs
written in  MATLAB 7+,  JAVA,  FORTRAN  and post-1985  ANSI
C.  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,  the
tricks are easy or unnecessary.  Examples show how well the
tricks work.


For details:
www.eecs.berkeley.edu/~wkahan/Math128/FloTrik.pdf