A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
SIAM Journal on Matrix Analysis and Applications
Recursiveness in matrix rational interpolation problems
Journal of Computational and Applied Mathematics - Special issue: ROLLS symposium
Shifted normal forms of polynomial matrices
ISSAC '99 Proceedings of the 1999 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
Computing the rank and a small nullspace basis of a polynomial matrix
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Normal forms for general polynomial matrices
Journal of Symbolic Computation
Computing hermite forms of polynomial matrices
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Efficient algorithms for order basis computation
Journal of Symbolic 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
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In this paper we give an efficient algorithm for computation of order basis of a matrix of power series. For a problem with an m x n input matrix over a field K, m ≤ n, and order σ, our algorithm uses O(MM(n, ⊂O~(nω⌈mσ/n⌉) field operations in B.K, where the soft-O notation O~ is Big O with log factors omitted and MM(n,d) denotes the cost of multiplying two polynomial matrices with dimension n and degree d. The algorithm extends earlier work of Storjohann, whose method can be used to find a subset of an order basis that is within a specified degree bound δ using O~(MM(n,δ)) field operations for δ≥⌈ mσ/n⌉.