Matrix analysis
Computing the singular value decompostion of a product of two matrices
SIAM Journal on Scientific and Statistical Computing
Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
The algebraic eigenvalue problem
The algebraic eigenvalue problem
LAPACK's user's guide
On graded QR decompositions of products of matrices
On graded QR decompositions of products of matrices
Exact computations of the inertia symmetric integer matrices
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Integer Smith form via the valence: experience with large sparse matrices from homology
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
On Wiedemann's Method of Solving Sparse Linear Systems
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
SIAM Review
The Complexity of the Inertia and Some Closure Properties of GapL
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Signature of symmetric rational matrices and the unitary dual of lie groups
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Certification of the QR factor R and of lattice basis reducedness
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
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Consider a rational matrix, particularly one whose entries have large numerators and denominators, but which is presented as a product of very sparse matrices with relatively small entries. We report on a numerical algorithm which computes the inertia of such a matrix in the nonsingular case and effectively exploits the product structure. We offer a symbolic/numeric hybrid algorithm for the singular case. We compare these methods with previous purely symbolic ones. By "purely symbolic" we refer to methods which restrict themselves to exact arithmetic and can assure that errors of approximation do not affect the results. Using an application in the study of Lie Groups as a plentiful source of examples of problems of this nature we explore the relative speeds of the numeric and hybrid methods as well as the range of applicability without error.