4 Citations
Eigenvalues, Smith normal form and determinantal ideals
- Mathematics
- 2019
Determinantal ideals of graphs generalize, among others, the spectrum and the Smith normal form (SNF) of integer matrices associated to graphs. In this work we investigate the relationship of the…
Smith Normal Form over Local Rings and Related Problems
- Computer Science, Mathematics
- 2017
The ultimate goal is to extend the applications of numerical algorithms for computing eigenvalues to computing the invariant factors of symbolic matrices as well as to design an algorithm for computing uniform samples from the nullspace.
C O ] 2 8 O ct 2 01 9 Eigenvalues , Smith normal form and determinantal ideals
- Mathematics
- 2019
Determinantal ideals of graphs generalize, among others, the spectrum and the Smith normal form (SNF) of integer matrices associated to graphs. In this work we investigate the relationship of the…
References
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p-adic Numbers, p-adic Analysis, and Zeta-Functions
- Mathematics
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P-adic numbers p-adic interpolation of the reimann zeta-function p-adic power series rationality of the zeta-function of a set of equations over a finite field (Part contents).
On Efficient Sparse Integer Matrix Smith Normal Form Computations
- Computer Science, MathematicsJ. Symb. Comput.
- 2001
We present a new algorithm to compute the Integer Smith normal form of large sparse matrices. We reduce the computation of the Smith form to independent, and therefore parallel, computations modulo…
A local construction of the Smith normal form of a matrix polynomial
- MathematicsJ. Symb. Comput.
- 2011
Exact Solution of Linear Equations Using P-Adie Expansions*
- Mathematics, Computer Science
- 2005
For matrices A and b with entries of bounded size and dimensions n x n and n x 1, this method can be implemented in time O(n3(logn) 2) which is better than methods previously used.
On Wiedemann's Method of Solving Sparse Linear Systems
- Computer ScienceAAECC
- 1991
Douglas Wiedemann’s (1986) landmark approach to solving sparse linear systems over finite fields provides the symbolic counterpart to non-combinatorial numerical methods for solving sparse linear…
Fast computation of Smith forms of sparse matrices over local rings
- Computer ScienceISSAC
- 2012
An algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small is given, and a method for dimension reduction while preserving the invariant Factors is described.