• Publications
  • Influence
Partial and Total Matrix Multiplication
  • A. Schönhage
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1 August 1981
TLDR
By combining Pan’s trilinear technique with a strong version of the compression theorem for the case of several disjoint matrix multiplications it is shown that multiplication of N \times N matrices (over arbitrary fields) is possible in time. Expand
Asymptotically Fast Algorithms for the Numerical Multiplication and Division of Polynomials with Complex Coeficients
TLDR
Under reasonable assumptions, polynomial multiplication and discrete Fourier transforms of length n and in l-bit precision are possible in time O(ψ (nl), and division of polynomials in O(n(l+n))). Expand
Quasi-GCD computations
  • A. Schönhage
  • Computer Science, Mathematics
  • J. Complex.
  • 1 October 1985
TLDR
Extended quasi-gcd computation means to find such h and additional cofactors u, ν such that uf + νg − h − h is an ϵ-approximate divisor of f and of g. Expand
Storage Modification Machines
TLDR
This paper gives a complete description of the SMM model and its real time equivalence to the so-called successor RAMS and shows the existence of an SMM that performs integer-multiplication in linear time. Expand
Fast algorithms for multiple evaluations of the riemann zeta function
The best previously know algorithm for evaluating the Riemann zeta function, ζ(σ+it), with σ bounded and t large to moderate accuracy was based on the Rienmann-Siegel formula and required on theExpand
Finding the Median
An algorithm is described which determines the median of n elements using in the worst case a number of comparisons asymptotic to 3n.
Factorization of Univariate Integer Polynomials by Diophantine Aproximation and an Improved Basis Reduction Algorithm
TLDR
All steps described in the preceding section for fixed m are certainly covered by the rather crude bound of \(O(m(n(n^{5 + \varepsilon } + n^3 (log|f|)^{2 + £3) (log | f|)}{2} ))\) bit operations, so the final time bound is obtained. Expand
A Lower Bound for the Length of Addition Chains
  • A. Schönhage
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1 June 1975
Abstract The length l of addition chains for z is shown to be bounded from below by log 2 z + log 2 s ( z )−2.13, where s ( z ) denotes the sum of the digits in the binary expansion of z . The proofExpand
On the Power of Random Access Machines
We study the power of deterministic successor RAM's with extra instructions like +,*,⋎ and the associated classes of problems decidable in polynomial time. Our main results are NP ... PTIME (+,*,⋎)Expand
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