# Search results for: Arne Storjohann

Journal of Symbolic Computation > 2018 > 85 > C > 224-246

Lecture Notes in Computer Science > Applied Algebra, Algebraic Algorithms and Error-Correcting Codes > Algorithms > 297-307

*ℤ*

_{ N }of integers modulo

*N*can be solved by transforming via elementary row operations an

*n*×

*m*input matrix

*A*to Howell form

*H*. The nonzero rows of

*H*give a canonical set of generators for the submodule of (

*ℤ*

_{ N })

^{ m }generated by the rows of

*A*. In this paper we present...

Journal of Complexity > 2015 > 31 > 2 > 162-173

computational complexity > 2015 > 24 > 4 > 777-821

*n*×

*n*integer matrix

*A*using $${({n^3(\log||A||+\log \kappa(A)))}^{1+o(1)}}$$ ( n 3 ( log | | A | | + log κ ( A ) ) ) 1 + o ( 1 ) bit operations. Here, $${||A||= \max_{ij}|A_{ij}|}$$ | | A | | = max i j | A i j | denotes the largest entry in absolute value, ...

Journal of Symbolic Computation > 2013 > 56 > Complete > 46-68

Journal of Symbolic Computation > 2012 > 47 > 4 > 422-453

Journal of Complexity > 2005 > 21 > 4 > 609-650

Journal of Symbolic Computation > 2003 > 36 > 3-4 > 613-648

Journal of Symbolic Computation > 2002 > 34 > 3 > 157-172

^{n×n}of any A∈Z

^{n×n}which requires an expected number of O(n

^{4}(logn+log|| A ||) +n

^{3}(logn+log|| A ||)

^{2}) word operations using standard integer and matrix arithmetic (where || A || =max

_{ij}| A

_{ij}|). This substantially improves on the fastest previously known algorithms...

Linear Algebra and Its Applications > 1998 > 282 > 1-3 > 25-45

Linear Algebra and Its Applications > 1997 > 253 > 1-3 > 155-173

^{n}

^{x}

^{n}of a nonsingular input matrix A Z [x]

^{n}

^{x}

^{n}. The algorithm requires an expected number of O ~ (n

^{3}d(d + n

^{2}log A )) bit operations (where A bounds the magnitude of all integer coefficients appearing in A, and d bounds the degrees of entries of...