scholarly journals INCOMPLETE CHOLESKY FACTORIZATION IN FIXED MEMORY WITH FLEXIBLE DROP-TOLERANCE STRATEGY

2014 ◽  
pp. 22-29
Author(s):  
Sergey Saukh
Keyword(s):  
Large Scale ◽  
Trust Region ◽  
Positive Definite ◽  
Cholesky Factorization ◽  
Systems Of Equations ◽  
Factor Matrix ◽  
Irregular Distribution ◽  
Tolerance Strategy ◽  
Incomplete Cholesky Factorization ◽  
Two Parameter

We propose an incomplete Cholesky factorization for the solution of large positive definite systems of equations and for the solution of large-scale trust region sub-problems. The factorization is based on the two- parameter (m, p) drop-tolerance strategy for insignificant elements in the incomplete factor matrix. The factorization proposed essentially reduces the negative processes of irregular distribution and accumulation of errors in factor matrix and provides the optimal rate of memory filling with essential nonzero elements. On the contrary to the known p - retain and t - drop-tolerance strategies, the (m, p) strategy allows to form the factor matrix in fixed memory.

A CONSTRAINT PRECONDITIONER FOR SOLVING SYMMETRIC POSITIVE DEFINITE SYSTEMS AND APPLICATION TO THE HELMHOLTZ EQUATIONS AND POISSON EQUATIONS

2010 ◽  
Vol 15 (3) ◽  
pp. 299-311 ◽  
Author(s):  
Zhuo-Hong Huang ◽  
Ting-Zhu Huang
Keyword(s):  
Numerical Experiments ◽  
Positive Definite ◽  
Cholesky Factorization ◽  
Helmholtz Equations ◽  
Poisson Equations ◽  
Symmetric Positive Definite ◽  
Incomplete Cholesky Factorization ◽  
Preconditioned Matrix ◽  
Factorization Methods ◽  
Number Of Iterations

In this paper, first, by using the diagonally compensated reduction and incomplete Cholesky factorization methods, we construct a constraint preconditioner for solving symmetric positive definite linear systems and then we apply the preconditioner to solve the Helmholtz equations and Poisson equations. Second, according to theoretical analysis, we prove that the preconditioned iteration method is convergent. Third, in numerical experiments, we plot the distribution of the spectrum of the preconditioned matrix M−1A and give the solution time and number of iterations comparing to the results of [5, 19].

A Class of Preconditioned TGHSS-Based Iteration Methods for Weakly Nonlinear Systems

2016 ◽  
Vol 6 (4) ◽  
pp. 367-383 ◽  
Author(s):  
Min-Li Zeng ◽  
Guo-Feng Zhang
Keyword(s):  
Nonlinear Systems ◽  
Iteration Method ◽  
Large Scale ◽  
Positive Definite ◽  
Weakly Nonlinear ◽  
Large Scale Systems ◽  
New Methods ◽  
Iteration Methods ◽  
Optimal Iterative Parameters ◽  
Two Parameter

AbstractIn this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSS-based iteration methods are proposed for solving weakly nonlinear systems based on separable property of the linear and nonlinear terms. The conditions for guaranteeing the local convergence are studied and the quasi-optimal iterative parameters are derived. Numerical experiments are implemented to show that the new methods are feasible and effective for large scale systems of weakly nonlinear systems.

scholarly journals Fast kernel k-means clustering using incomplete Cholesky factorization

2021 ◽  
Vol 402 ◽  
pp. 126037
Author(s):  
Li Chen ◽  
Shuisheng Zhou ◽  
Jiajun Ma ◽  
Mingliang Xu
Keyword(s):  
Cholesky Factorization ◽  
Incomplete Cholesky Factorization

scholarly journals Using a Cable-Driven Parallel Robot with Applications in 3D Concrete Printing

2021 ◽  
Vol 11 (2) ◽  
pp. 563
Author(s):  
Tuong Phuoc Tho ◽  
Nguyen Truong Thinh
Keyword(s):  
3D Printing ◽  
Large Scale ◽  
Trust Region ◽  
Parallel Robot ◽  
Inverse Kinematic ◽  
Programming Algorithm ◽  
Construction Time ◽  
Inverse Kinematic Problem ◽  
Robot Configuration ◽  
Printing Method

In construction, a large-scale 3D printing method for construction is used to build houses quickly, based on Computerized Aid Design. Currently, the construction industry is beginning to apply quite a lot of 3D printing technologies to create buildings that require a quick construction time and complex structures that classical methods cannot implement. In this paper, a Cable-Driven Parallel Robot (CDPR) is described for the 3D printing of concrete for building a house. The CDPR structures are designed to be suitable for 3D printing in a large workspace. A linear programming algorithm was used to quickly calculate the inverse kinematic problem with the force equilibrium condition for the moving platform; this method is suitable for the flexible configuration of a CDPR corresponding to the various spaces. Cable sagging was also analyzed by the Trust-Region-Dogleg algorithm to increase the accuracy of the inverse kinematic problem for controlling the robot to perform basic trajectory interpolation movements. The paper also covers the design and analysis of a concrete extruder for the 3D printing method. The analytical results are experimented with based on a prototype of the CDPR to evaluate the work ability and suitability of this design. The results show that this design is suitable for 3D printing in construction, with high precision and a stable trajectory printing. The robot configuration can be easily adjusted and calculated to suit the construction space, while maintaining rigidity as well as an adequate operating space. The actuators are compact, easy to disassemble and move, and capable of accommodating a wide variety of dimensions.

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