نتایج جستجو برای: elementary block matrix operations

تعداد نتایج: 687288  

Journal: :Sci. Comput. Program. 1999
David S. Wise

A new formulation for LU decomposition allows efficient representation of intermediate matrices while eliminating blocks of various sizes, i.e. during “undulantblock” elimination. Its efficiency arises from its design for block encapsulization, implicit in data structures that are convenient both for process scheduling and for memory management. Row/column permutations that can destroy such enc...

2008
Tad Hogg Carlos Mochon Wolfgang Polak Eleanor Rieffel

We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of the phase adjustments to block matrix transformations. These operations generalize those used in proposed quantum search algorithms.

Journal: :I. J. Network Security 2009
Jorge Nakahara Élcio Abrahão

This paper proposes a new, large diffusion layer for the AES block cipher. This new layer replaces the ShiftRows and MixColumns operations by a new involutory matrix in every round. The objective is to provide complete diffusion in a single round, thus sharply improving the overall cipher security. Moreover, the new matrix elements have low Hamming-weight in order to provide equally good perfor...

2001
A. Megretski

Let M be a complex matrix of rank one, i.e. M = pq′ where p, q are complex nby-1 matrices and ′ denotes Hermitean conjugation. Let μC(M) and μR(M) denote the structured singular values μ(M,∆) of M defined with ∆ = ∆C and ∆ = ∆R respectively, where ∆C is the cone of all diagonal matrices with complex entries, and ∆R is the cone of all diagonal matrices with real entries. (a) Express μC(M) and μR...

Journal: :CoRR 2012
Dohy Hong Fabien Mathieu Gérard Burnside

In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We show how this can be applied to prove and improve the convergence of a fixed point problem associated to the matrix iteration scheme, including for distributed ...

2004
N. Peter Drakenberg

We describe a datatype for (dense) matrices whose primitive operations are decomposition and composition (of submatrices), as opposed to indexed element access which is the primitive operation on conventional arrays. Using the composition and decomposition operations it is for example possible to express both recursive and traditional block matrix algorithms (e.g., Cholesky factorization, QR-fa...

2013
Alessandro Febretti

In this project, we had to implement a parallel solver for linear equation systems, using a technique known as Gaussian elimination (GE). As with many other algorithms for solving linear equation systems, GE is performed on the matrix representation of the system, Ax = b, where A is the coefficient matrix and b is the vector of known values. GE works by applying a set of elementary row operatio...

Journal: :Archive of Formal Proofs 2015
Jose Divasón Jesús Aransay

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...

Journal: :J. Comput. Science 2013
Sebastian F. Walter Lutz Lehmann

Many programs for scienti c computing in Python are based on NumPy and therefore make heavy use of numerical linear algebra (NLA) functions, vectorized operations, slicing and broadcasting. AlgoPy provides the means to compute derivatives of arbitrary order and Taylor approximations of such programs. The approach is based on a combination of univariate Taylor polynomial arithmetic and matrix ca...

Journal: :Proceedings of the American Mathematical Society 1955

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