Applied & computational complex analysis: power series integration conformal mapping location of zero
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Computing with Formal Power Series
ACM Transactions on Mathematical Software (TOMS)
On the power series solution of a system of algebraic equations
ACM SIGSAM Bulletin
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
All Algebraic Functions Can Be Computed Fast
Journal of the ACM (JACM)
Algebraic algorithms using p-adic constructions
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
On the Check of Accuracy of the Coefficients of Formal Power Series
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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The analytic concepts of approximation, convergence, differentiation, and Taylor series expansion are applied and interpreted in the context of an abstract power series domain. Newton's method is then shown to be applicable to solving for a power series root of a polynomial with power series coefficients, resulting in fast algorithms for a variety of power series manipulation problems. Sample applications of a FORMAC implementation of Newton's method as an algebraic algorithm are presented.