Publication Details
Title: Can We Utilize the Cancellation of the Most Significant Digits?
Author: V. Pan
Group: ICSI Technical Reports
Date: December 1992
PDF: http://www.icsi.berkeley.edu/pubs/techreports/tr-92-061.pdf
Overview:
If the sum of several positive and negative numbers has a small magnitude, relative to the magnitudes of the summands, then we show how to decrease the precision of the computation of this sum (without affecting the output precision). Furthermore, if the magnitude of the inner product of two vectors is small and if one of them is filled with "short" binary numbers, each represented with only a few bits, then we decrease the precision of the computation of such an inner product (without affecting the output precision), and we extend this result to the iterative improvement algorithm for a linear system of equations, whose coefficients are represented by "short" binary numbers. We achieve this by truncating both the least and the most significant digits of the operands, according to our new scheme of "backward binary segmentation."
Bibliographic Information:
ICSI Technical Report TR-92-061
Bibliographic Reference:
V. Pan. Can We Utilize the Cancellation of the Most Significant Digits?. ICSI Technical Report TR-92-061, December 1992
Author: V. Pan
Group: ICSI Technical Reports
Date: December 1992
PDF: http://www.icsi.berkeley.edu/pubs/techreports/tr-92-061.pdf
Overview:
If the sum of several positive and negative numbers has a small magnitude, relative to the magnitudes of the summands, then we show how to decrease the precision of the computation of this sum (without affecting the output precision). Furthermore, if the magnitude of the inner product of two vectors is small and if one of them is filled with "short" binary numbers, each represented with only a few bits, then we decrease the precision of the computation of such an inner product (without affecting the output precision), and we extend this result to the iterative improvement algorithm for a linear system of equations, whose coefficients are represented by "short" binary numbers. We achieve this by truncating both the least and the most significant digits of the operands, according to our new scheme of "backward binary segmentation."
Bibliographic Information:
ICSI Technical Report TR-92-061
Bibliographic Reference:
V. Pan. Can We Utilize the Cancellation of the Most Significant Digits?. ICSI Technical Report TR-92-061, December 1992