Details:
Title  Outputsensitive modular algorithms for polynomial matrix normal forms  Author(s)  Howard Cheng, George Labahn  Type  Article in Journal  Abstract  We give modular algorithms to compute rowreduced forms, weak Popov forms, and Popov forms of polynomial matrices, as well as the corresponding unimodular transformation matrices. Our algorithms improve on existing fractionfree algorithms. In each case, we define lucky homomorphisms, determine the appropriate normalization, as well as bound the number of homomorphic images required. The algorithms have the advantage that they are outputsensitive; that is, the number of homomorphic images required depends on the size of the output. Furthermore, there is no need to verify the result by trial division or multiplication. Our algorithms can be used to compute normalized onesided greatest common divisors and least common multiples of polynomial matrices, along with irreducible matrixfraction descriptions of matrix rational functions. When our algorithm is used to compute polynomial greatest common divisors, we obtain a new outputsensitive modular algorithm.  Keywords  Matrices, Rowreduced form, Weak Popov form, Popov form, Modular algorithm  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717107000417 
Language  English  Journal  Journal of Symbolic Computation  Volume  42  Number  7  Pages  733  750  Year  2007  Edition  0  Translation 
No  Refereed 
No 
