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Reports Year : 2000

## Speeding up the inversion of power series

(1) , (1)
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Guillaume Hanrot
• Function : Author
• PersonId : 831392
Paul Zimmermann

#### Abstract

We present a new algorithm to compute the $n$ middle coefficients of a $2n \times n$ product in $K(n)$ ring operations, where $K(n)$ is the number of operations needed by Karatsuba's algorithm for a full $n \times n$ product. Used in Newton iteration, and together with previous work of Mulders, Karp and Markstein, this algorithm enables one to compute an inverse in $\sim 0.904 \, K(n)$ operations, a quotient in $\sim 1.173 \, K(n)$ operations, and a square root in $\sim 0.891 \, K(n)$ operations. These results apply both to power series and polynomials.

#### Domains

Computer Science [cs] Other [cs.OH]

### Dates and versions

inria-00099294 , version 1 (26-09-2006)

### Identifiers

• HAL Id : inria-00099294 , version 1

### Cite

Guillaume Hanrot, Paul Zimmermann. Speeding up the inversion of power series. [Intern report] A00-R-067 || hanrot00a, 2000, 8 p. ⟨inria-00099294⟩

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