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William "Velvel" Morton Kahan (born June 5, 1933) is a Canadian mathematician and computer scientist, who received the Turing Award in 1989 for "his fundamental contributions to numerical analysis", was named an ACM Fellow in 1994, and inducted into the National Academy of Engineering in 2005.
William Velvel Kahan (Toronto, 5 de junho de 1933) é um matemático e informático canadense. Sua principal área de interesse é a análise numérica. Formado pela Universidade de Toronto em 1954, onde obteve um mestrado em matemática, em 1956, com doutorado em 1958.
11 de set. de 2019 · William Kahan Ph.D. (Math., University of Toronto, 1958) Professor Emeritus of Mathematics, and of E.E. & Computer Science 863 Evans Hall (Math), and 411 Soda Hall (CS) Now that I am "retired", I work in my offices sporadically at least once or twice a week during each semester. Phone: (510) 642-5638 (rings in both offices)
For his fundamental contributions to numerical analysis. One of the foremost experts on floating-point computations. Kahan has dedicated himself to "making the world safe for numerical computations!" William Kahan was born in Canada in 1933 and grew up around Toronto in a family of Jewish immigrants.
- The Algorithm
- Accuracy
- Further Enhancements
- Alternatives
- Possible Invalidation by Compiler Optimization
- Support by Libraries
In pseudocode, the algorithm will be: This algorithm can also be rewritten to use the Fast2Sumalgorithm:
A careful analysis of the errors in compensated summation is needed to appreciate its accuracy characteristics. While it is more accurate than naive summation, it can still give large relative errors for ill-conditioned sums. Suppose that one is summing n {\displaystyle n} values x i {\displaystyle x_{i}} , for i = 1 , … , n {\displaystyle i=1,\,\l...
Neumaier introduced an improved version of Kahan algorithm, which he calls an "improved Kahan–Babuška algorithm", which also covers the case when the next term to be added is larger in absolute value than the running sum, effectively swapping the role of what is large and what is small. In pseudocode, the algorithm is: This enhancement is similar t...
Although Kahan's algorithm achieves O ( 1 ) {\displaystyle O(1)} error growth for summing n numbers, only slightly worse O ( log n ) {\displaystyle O(\log n)} growth can be achieved by pairwise summation: one recursively divides the set of numbers into two halves, sums each half, and then adds the two sums. This has the advantage of requiring the...
In principle, a sufficiently aggressive optimizing compiler could destroy the effectiveness of Kahan summation: for example, if the compiler simplified expressions according to the associativityrules of real arithmetic, it might "simplify" the second step in the sequence 1. t = sum + y; 2. c = (t - sum) - y; to 1. c = ((sum + y) - sum) - y; and the...
In general, built-in "sum" functions in computer languages typically provide no guarantees that a particular summation algorithm will be employed, much less Kahan summation.[citation needed] The BLAS standard for linear algebra subroutines explicitly avoids mandating any particular computational order of operations for performance reasons,and BLAS ...
1 de mai. de 2024 · William Kahan (born June 5, 1933, Toronto, Ontario, Canada) is a Canadian mathematician and computer scientist and winner of the 1989 A.M. Turing Award, the highest honour in computer science, for his “fundamental contributions to numerical analysis .”.
He developed a program called "paranoia' in the 1980s to test for potential floating point bugs and developed the Kaham summation algorithm which helps minimize errors introduced when adding a sequences of finite precision floating point numbers. Kahan won the ACM A.M. Turing Award in 1989.
