The Harrow-Hassidim-Lloyd quantum algorithm was proposed to solve linear systems of equations $A\vec{x} = \vec{b}$ and it is the core various applications. However, there not an explicit circuit for subroutine which maps inverse problem matrix $A$ into ancillary qubit. This makes challenging implementation in current devices, forcing us use hybrid approaches. Here, we propose a systematic manne...

In this thesis I present a new algorithm OPT for matrix inversion that builds on a matrix multiplication subroutine. It is combined of Strassen’s matrix inversion algorithm and Newton approximation. OPT overcomes the linear lower bound in parallel runtime of Strassen’s inversion algorithm and traditional Gaussian elimination without the log-factor more work of Newton approximation. In particula...

The objective stress rates used in most commercial finite element programs are the Jaumann rate of Kirchhoff stress, Jaumann rates of Cauchy stress, or Green–Naghdi rate. The last two were long ago shown not to be associated by work with any finite strain tensor, and the first has often been combined with tangential moduli not associated by work. The error in energy conservation was thought to ...

Up to now a large number of models have been developed to measure or predict the damage in equipments. Some of these models have been implemented in ABAQUS software. To implement damage parameters in the software, it is necessary to perform complex and expensive practical tests. One of these damage models is Forming Limit Diagram (FLD).The purpose of this research is deriving required parameter...

the paper aims at investigating the effects of chemical reaction and thermal radiation on the steady two-dimensional laminar flow of viscous incompressible electrically conducting micropolar fluid past a stretching surface embedded in a non-darcian porous medium. the radiative heat flux is assumed to follow rosseland approximation. the governing equations of momentum, angular momentum, energy, ...

This work is part of a joint project of ANU and Fujitsu Ltd. Japan for the development of vector and parallel numerical algorithms and software. The results will be included in the Fujitsu Scientiic Subroutine Library. Coding and testing is done in cooperation with

Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint diagonalization to low-rank and asymmetric matrices, and we also provide extensions to the perturbation analysis of these methods. Our results allow joint diagonalizati...

A submodular polyhedron is a polyhedron associated with a submodular function. This paper presents a strongly polynomial time algorithm for line search in submodular polyhedra with the aid of a fully combinatorial algorithm for submodular function minimization as a subroutine. The algorithm is based on the parametric search method proposed by Megiddo.

The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the l1-regularized (possibly not strongly) convex QP that terminate at an optimal solution in a finite number of iterations. At each iteration, our methods first identify a face of an orthan...

We analyze the damage initiation, damage progression, and failure during 3-dimensional (3-D) elastoplastic deformations of a fiber reinforced polymeric laminated composite impacted by a low speed rigid sphere, and compare computed results with experimental findings available in the literature. Damage is assumed to initiate when one of Hashin’s failure criteria is satisfied, and its evolution is...