A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
SIAM Journal on Matrix Analysis and Applications
Computing Popov and Hermite forms of polynomial matrices
ISSAC '96 Proceedings of the 1996 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
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
On the complexity of polynomial matrix computations
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
On lattice reduction for polynomial matrices
Journal of Symbolic Computation
Modern Computer Algebra
Normal forms for general polynomial matrices
Journal of Symbolic Computation
Triangular x-basis decompositions and derandomization of linear algebra algorithms over K[x]
Journal of Symbolic Computation
Triangular x-basis decompositions and derandomization of linear algebra algorithms over K[x]
Journal of Symbolic 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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This paper gives gives a deterministic algorithm to transform a row reduced matrix to canonical Popov form. Given as input a row reduced matrix R over K[x], K a field, our algorithm computes the Popov form in about the same time as required to multiply together over K[x] two matrices of the same dimension and degree as R. We also show that the problem of transforming a row reduced matrix to Popov form is at least as hard as polynomial matrix multiplication.