ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
ACM Transactions on Mathematical Software (TOMS)
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Fraction-free computation of matrix Padé systems
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
An algorithm for computing exponential solutions of first order linear differential systems
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
A reduction algorithm for matrices depending on a parameter
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Shifted normal forms of polynomial matrices
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Fraction-free row reduction of matrices of skew polynomials
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
On the complexity of polynomial matrix computations
ISSAC '03 Proceedings of the 2003 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
D-finiteness: algorithms and applications
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
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
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
Solving structured linear systems with large displacement rank
Theoretical Computer Science
Journal of Symbolic Computation
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
Normal forms for general polynomial matrices
Journal of Symbolic Computation
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Optimization techniques for small matrix multiplication
Theoretical Computer Science
Journal of 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
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
Trading order for degree in creative telescoping
Journal of Symbolic Computation
Journal of Symbolic 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)
Guessing singular dependencies
Journal of Symbolic Computation
Hi-index | 0.00 |
Recently, a uniform approach was given by B. Beckermann and G. Labahn [Numer. Algorithms, 3 (1992), pp. 45-54] for different concepts of matrix-type Pade approximants, such as descriptions of vector and matrix Pade approximants along with generalizations of simultaneous and Hermite Pade approximants. The considerations in this paper are based on this generalized form of the classical scalar Hermite Pade approximation problem, power Hermite Pade approximation. In particular, this paper studies the problem of computing these new approximants. A recurrence relation is presented for the computation of a basis for the corresponding linear solution space of these approximants. This recurrence also provides bases for particular subproblems. This generalizes previous work by Van Barel and Bultheel and, in a more general form, by Beckermann. The computation of the bases has complexity ${\cal O}(\sigma^{2})$, where $\sigma$ is the order of the desired approximant and requires no conditions on the input data. A second algorithm using the same recurrence relation along with divide-and-conquer methods is also presented. When the coefficient field allows for fast polynomial multiplication, this second algorithm computes a basis in the superfast complexity ${\cal O}(\sigma \log^{2})$. In both cases the algorithms are reliable in exact arithmetic. That is, they never break down, and the complexity depends neither on any normality assumptions nor on the singular structure of the corresponding solution table. As a further application, these methods result in fast (and superfast) reliable algorithms for the inversion of striped Hankel, layered Hankel, and (rectangular) block-Hankel matrices.