Computational complexity of computing polynomials over the fields of real and complex numbers

Authors:
V. Ya. Pan
Affiliations:
-
Venue:
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Year:
1978

Citing 3
Cited 0

The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms

The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Evaluation of polynomials by computer

Communications of the ACM
Combining dimensionality and rate of growth arguments for establishing lower bounds on the number of multiplications

STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing

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Abstract

Fast computation of polynomials of 1 variable in the fields R and C of real and complex numbers is considered. The optimal schemes of computation with preconditioning (that is, the schemes involving the minimal number of arithmetic operations without counting preliminary treatment of coefficients) for evaluation in C are presented. The schemes which are close to optimal ones are presented for evaluation in R. The difference between the complexity of computation in R and in C is established. A new generalization of the problem is presented.