On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm
Mathematics of Computation
A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
SIAM Journal on Matrix Analysis and Applications
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Nearly optimal algorithms for canonical matrix forms
Nearly optimal algorithms for canonical matrix forms
Computing Popov and Hermite forms of polynomial matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Matrix-free linear system solving and applications to symbolic computation
Matrix-free linear system solving and applications to symbolic computation
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Black box linear algebra with the linbox library
Black box linear algebra with the linbox library
On lattice reduction for polynomial matrices
Journal of Symbolic Computation
High-order lifting and integrality certification
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
FFPACK: finite field linear algebra package
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Essentially optimal computation of the inverse of generic polynomial matrices
Journal of Complexity - Special issue: Foundations of computational mathematics 2002 workshops
Computing the rank and a small nullspace basis of a polynomial matrix
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Polynomial evaluation and interpolation on special sets of points
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Solving sparse rational linear systems
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
A block Wiedemann rank algorithm
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Solving structured linear systems of large displacement rank
ACM Communications in Computer Algebra
Output-sensitive modular algorithms for polynomial matrix normal forms
Journal of Symbolic Computation
Solving toeplitz- and vandermonde-like linear systems with large displacement rank
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Faster inversion and other black box matrix computations using efficient block projections
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Some recent progress in exact linear algebra and related questions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Parallel computation of the rank of large sparse matrices from algebraic K-theory
Proceedings of the 2007 international workshop on Parallel symbolic computation
Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK Packages
ACM Transactions on Mathematical Software (TOMS)
Solving structured linear systems with large displacement rank
Theoretical Computer Science
Fraction-free computation of simultaneous padé approximants
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Efficient computation of order bases
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Polynomial evaluation and interpolation on special sets of points
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Adaptive niche radii and niche shapes approaches for niching with the cma-es
Evolutionary Computation
Factoring polynomials over global fields II
Journal of Symbolic Computation
Validated numerical computation of the L∞-norm for linear dynamical systems
Journal of Symbolic Computation
Normal forms for general polynomial matrices
Journal of Symbolic Computation
Exact sparse matrix-vector multiplication on GPU's and multicore architectures
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Recent progress in linear algebra and lattice basis reduction
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Computing hermite forms of polynomial matrices
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Normalization of row reduced matrices
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Triangular x-basis decompositions and derandomization of linear algebra algorithms over K[x]
Journal of Symbolic Computation
Efficient algorithms for order basis computation
Journal of Symbolic Computation
Simplified high-speed high-distance list decoding for alternant codes
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Optimally robust private information retrieval
Security'12 Proceedings of the 21st USENIX conference on Security symposium
The M4RIE library for dense linear algebra over small fields with even characteristic
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Computing minimal nullspace bases
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Computing column bases of polynomial matrices
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
On the matrix berlekamp-massey algorithm
ACM Transactions on Algorithms (TALG)
Relaxing order basis computation
ACM Communications in Computer Algebra
Block Wiedemann algorithm on multicore architectures
ACM Communications in Computer Algebra
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We study the link between the complexity of polynomial matrix multiplication and the complexity of solving other basic linear algebra problems on polynomial matrices. By polynomial matrices we mean ntimes n matrices in K[x] of degree bounded by d, with K a commutative field. Under the straight-line program model we show that multiplication is reducible to the problem of computing the coefficient of degree d of the determinant. Conversely, we propose algorithms for minimal approximant computation and column reduction that are based on polynomial matrix multiplication; for the determinant, the straight-line program we give also relies on matrix product over K[x] and provides an alternative to the determinant algorithm of [16, 17]. We further show that all these problems can be solved in particular in O (ω) operations in K. Here the "soft O" notation O indicates some missing log (nd) factors and ω is the exponent of matrix multiplication over K.