IBM Journal of Research and Development
IBM Skip to main content
  Home     Products & services     Support & downloads     My account  

  Select a country  
Journals Home  
  Systems Journal  
Journal of Research
and Development
    Current Issue  
    Recent Issues  
    Papers in Progress  
    Recent publications  
    Author's Guide  
  Contact Us  
  Related links:  
     IBM Research  

IBM Journal of Research and Development  
Volume 27, Number 6, Page 582 (1983)
Nontopical Issue
  Full article: arrowPDF   arrowCopyright info


A Class of Numerical Methods for the Computation of Pythagorean Sums

by A. A. Dubrulle
Moler and Morrison have described an iterative algorithm for the computation of the Pythagorean sum (a2+b2)½ of two real numbers a and b. This algorithm is immune to unwarranted floating-point overflows, has a cubic rate of convergence, and is easily transportable. This paper, which shows that the algorithm is essentially Halley's method applied to the computation of square roots, provides a generalization to any order of convergence. Formulas of orders 2 through 9 are illustrated with numerical examples. The generalization keeps the number of floating-point divisions constant and should be particularly useful for computation in high-precision floating-point arithmetic.
Related Subjects: Algorithms; Computational methods; Mathematics (applied)