Degeneration of structured integer matrices modulo an integer
نویسندگان
چکیده
منابع مشابه
Degeneration of Structured Integer Matrices Modulo an Integer
Hensel’s lifting modulo a prime q is a customary means of the solution of an integer or rational linear system of equations. In combination with some effective numerical algorithms this technique enables solution in nearly optimal time in the case of most popular structured inputs. Practically one can further benefit from choosing q = 2 for a proper positive integer v and performing binary comp...
متن کاملTR-2008007: Degeneration of Structured Integer Matrices Modulo an Integer
Hensel’s lifting modulo a prime q is a customary means of the solution of an integer or rational linear system of equations. In combination with some effective numerical algorithms this technique enables solution in nearly optimal time in the case of most popular structured inputs. Practically one can further benefit from choosing q = 2 for a proper positive integer v and performing binary comp...
متن کاملOn the WZ Factorization of the Real and Integer Matrices
The textit{QIF} (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ} factorization. The WZ factorization can be faster than the textit{LU} factorization because, it performs the simultaneous evaluation of two columns or two rows. Here, we present a method for computing the real and integer textit{WZ} and textit{ZW} factoriz...
متن کاملUnified Nearly Optimal Algorithms for Structured Integer Matrices and Polynomials
We seek the solution of banded, Toeplitz, Hankel, Vandermonde, Cauchy and other structured linear systems of equations with integer coefficients. By combining Hensel’s symbolic lifting with either divide-and-conquer algorithms or numerical iterative refinement, we unify the solution for all these structures. We yield the solution in nearly optimal randomized Boolean time, which covers both solu...
متن کاملEstimating Tree-Structured Covariance Matrices via Mixed-Integer Programming
We present a novel method for estimating tree-structured covariance matrices directly from observed continuous data. Specifically, we estimate a covariance matrix from observations of p continuous random variables encoding a stochastic process over a tree with p leaves. A representation of these classes of matrices as linear combinations of rank-one matrices indicating object partitions is used...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.06.020