Hermite polynomial normal transformation for structural reliability analysis

ENHANCING WEIGHTED UNIFORM SIMULATION FOR STRUCTURAL RELIABILITY ANALYSIS

Weighted Uniform Simulation (WUS) is recently presented as one of the efficient simulation methods to obtain structural failure probability and most probable point (MPP). This method requires initial assumptions of failure probability to obtain results. Besides, it has the problem of variation in results when it conducted with few samples. In the present study three strategies have been present...

Preconditioning of Rectangular Polynomial Matrices for Eecient Hermite Normal Form Computation

We present a Las Vegas probabalistic algorithm for reducing the computation of Hermite normal forms of rectangular polynomial matrices. In particular, the problem of computing the Hermite normal form of a rectangular m n matrix (with m > n) reduces to that of computing the Hermite normal form of a matrix of size (n + 1) n having entries of similar coeecient size and degree. The main cost of the...

Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix

A fast, deterministic algorithm for computing a Hermite Normal Form of a polynomial matrix

Given a square, nonsingular matrix of univariate polynomials F ∈ K[x] over a field K, we give a fast, deterministic algorithm for finding the Hermite normal form of F with complexity O (nωd) where d is the degree of F. Here soft-O notation is Big-O with log factors removed and ω is the exponent of matrix multiplication. The method relies of a fast algorithm for determining the diagonal entries ...

Hermite Normal Form

The Hermite Normal Form is a canonical matrix analogue of Reduced Echelon Form, but involving matrices over more general rings. In this work we formalise an algorithm to compute the Hermite Normal Form of a matrix by means of elementary row operations, taking advantage of the Echelon Form AFP entry. We have proven the correctness of such an algorithm and refined it to immutable arrays. Furtherm...