scholarly journals Improved Qrginv Algorithm for Computing Moore-Penrose Inverse Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Alireza Ataei
Keyword(s):  
Numerical Experiments ◽  
Computation Time ◽  
Computational Method ◽  
Real Matrix ◽  
Pseudoinverse Matrix ◽  
Arbitrary Matrix ◽  
Pseudo Inverse

Katsikis et al. presented a computational method in order to calculate the Moore-Penrose inverse of an arbitrary matrix (including singular and rectangular) (2011). In this paper, an improved version of this method is presented for computing the pseudo inverse of an m×n real matrix A with rank r>0. Numerical experiments show that the resulting pseudoinverse matrix is reasonably accurate and its computation time is significantly less than that obtained by Katsikis et al.

scholarly journals A General and Numerically Efficient Framework to Design Sector-Type and Cylindrical Counterweights for Balancing of Planar Linkages

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
B. Demeulenaere ◽  
M. Verschuure ◽  
J. Swevers ◽  
J. De Schutter
Keyword(s):  
Iterative Procedure ◽  
Numerical Experiments ◽  
Optimization Problems ◽  
Computation Time ◽  
Efficient Design ◽  
Convex Optimization Problems ◽  
Sector Type ◽  
Planar Linkages ◽  
Driving Torque ◽  
Shaking Moment

This paper extends previous work concerning convex reformulations of counterweight balancing by developing a general and numerically efficient design framework for counterweight balancing of arbitrarily complex planar linkages. At the numerical core of the framework is an iterative procedure, in which successively solving three convex optimization problems yields practical counterweight shapes in typically less than 1 CPU s. Several types of counterweights can be handled. The iterative procedure allows minimizing and/or constraining shaking force, shaking moment, driving torque, and bearing forces. Numerical experiments demonstrate the numerical superiority (in terms of computation time and balancing result) of the presented framework compared to existing approaches.

AN IMPROVED REDUCTION METHOD FOR THE ROBUST OPTIMIZATION OF THE ASSIGNMENT PROBLEM

2012 ◽  
Vol 29 (05) ◽  
pp. 1250032 ◽  
Author(s):  
BYUNGJUN YOU ◽  
DAISUKE YOKOYA ◽  
TAKEO YAMADA
Keyword(s):  
Lower Bound ◽  
Exact Solutions ◽  
Upper Bound ◽  
Assignment Problem ◽  
Numerical Experiments ◽  
Reduction Method ◽  
Computation Time ◽  
Approximate Solutions ◽  
Cpu Time ◽  
Surrogate Relaxation

We are concerned with a variation of the assignment problem, where the assignment costs differ under different scenarios. We give a surrogate relaxation approach to derive a lower bound and an upper bound quickly, and show that the pegging test known for zero–one programming problems is also applicable to this problem. Next, we discuss how the computation time for pegging can be shortened by taking the special structure of the assignment problem into account. Finally, through numerical experiments we show that the developed method finds exact solutions for instances with small number of scenarios in relatively small CPU time, and good approximate solutions in case of many scenarios.

scholarly journals Parallel Implementation of Katsevich's FBP Algorithm

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
Jiansheng Yang ◽  
Xiaohu Guo ◽  
Qiang Kong ◽  
Tie Zhou ◽  
Ming Jiang
Keyword(s):  
Numerical Experiments ◽  
Parallel Implementation ◽  
Cone Beam Ct ◽  
Computation Time ◽  
Cone Beam ◽  
Filtered Backprojection ◽  
Typical Experiment ◽  
Linux Cluster ◽  
Parallel Reconstruction ◽  
Reconstruction Time

For spiral cone-beam CT, parallel computing is an effective approach to resolving the problem of heavy computation burden. It is well known that the major computation time is spent in the backprojection step for either filtered-backprojection (FBP) or backprojected-filtration (BPF) algorithms. By the cone-beam cover method [1], the backprojection procedure is driven by cone-beam projections, and every cone-beam projection can be backprojected independently. Basing on this fact, we develop a parallel implementation of Katsevich's FBP algorithm. We do all the numerical experiments on a Linux cluster. In one typical experiment, the sequential reconstruction time is 781.3 seconds, while the parallel reconstruction time is 25.7 seconds with 32 processors.

Research on MPI-Based Parallel Max-Min Ant System

2012 ◽  
Vol 198-199 ◽  
pp. 1321-1326 ◽  
Author(s):  
Yu Liu ◽  
Guo Dong Wu
Keyword(s):  
Combinatorial Optimization ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
Computation Time ◽  
Traveling Salesman ◽  
Ant System ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

When solving large scale combinatorial optimization problems, Max-Min Ant System requires long computation time. MPI-based Parallel Max-Min Ant System described in this paper can ensure the quality of the solution, as well as reduce the computation time. Numerical experiments on the multi-node cluster system show that when solving the traveling salesman problem, MPI-based Parallel Max-Min Ant System can get better computational efficiency.

scholarly journals Singular Factorization of an Arbitrary Matrix

2017 ◽  
Vol 12 (1) ◽  
pp. 77-86
Author(s):  
Gyan Bahadur Thapa ◽  
P. Lam-Estrada ◽  
J. López-Bonilla
Keyword(s):  
Singular Value Decomposition ◽  
Linear Systems ◽  
Singular Value ◽  
Arbitrary Matrix ◽  
Natural Manner ◽  
Value Decomposition ◽  
Pseudo Inverse

In this paper, we study the Singular Value Decomposition of an arbitrary matrix Anxm, especially its subspaces of activation, which leads in natural manner to the pseudo inverse of Moore -Bjenhammar - Penrose. Besides, we analyze the compatibility of linear systems and the uniqueness of the corresponding solution and our approach gives the Lanczos classification for these systems.Journal of the Institute of Engineering, 2016, 12(1): 77-86 

Computational Assignment of Protein Backbone NMR Peaks by Efficient Bounding and Filtering

2003 ◽  
Vol 01 (02) ◽  
pp. 387-409 ◽  
Author(s):  
Guohui Lin ◽  
Dong Xu ◽  
Zhi-Zhong Chen ◽  
Tao Jiang ◽  
Jianjun Wen ◽  
...  
Keyword(s):  
Computation Time ◽  
Search Space ◽  
Nmr Resonance Assignment ◽  
Computational Method ◽  
General Situation ◽  
Matching Problem ◽  
Bipartite Matching ◽  
Nmr Data ◽  
Peak Assignment ◽  
Key Steps

NMR resonance assignment is one of the key steps in solving an NMR protein structure. The assignment process links resonance peaks to individual residues of the target protein sequence, providing the prerequisite for establishing intra- and inter-residue spatial relationships between atoms. The assignment process is tedious and time-consuming, which could take many weeks. Though there exist a number of computer programs to assist the assignment process, many NMR labs are still doing the assignments manually to ensure quality. This paper presents a new computational method based on the combination of a suite of algorithms for automating the assignment process, particularly the process of backbone resonance peak assignment. We formulate the assignment problem as a constrained weighted bipartite matching problem. While the problem, in the most general situation, is NP-hard, we present an efficient solution based on a branch-and-bound algorithm with effective bounding techniques using two recently introduced approximation algorithms. We also devise a greedy filtering algorithm for reducing the search space. Our experimental results on 70 instances of (pseudo) real NMR data derived from 14 proteins demonstrate that the new solution runs much faster than a recently introduced (exhaustive) two-layer algorithm and recovers more correct peak assignments than the two-layer algorithm. Our result demonstrates that integrating different algorithms can achieve a good tradeoff between backbone assignment accuracy and computation time.

A Study on Facility Layout Using Evolution Strategies in Case of Different Shapes and Areas of Facilities

2012 ◽  
Author(s):  
Naoki Hirabayashi ◽  
Kazuko Morizawa
Keyword(s):  
Relative Error ◽  
Numerical Experiments ◽  
Facility Layout ◽  
Computation Time ◽  
Adaptive Strategy ◽  
The Other ◽  
Evolution Strategies ◽  
Average Relative Error ◽  
Different Shapes ◽  
Excellent Property

Evolution Strategies have more excellent property than the other existing metaheuristics in a sense of easiness of coding and its manageability of self-adaptive strategy, Hirabayashi et al. proposed a facility layout method using Evolution Strategies for obtaining near optimum solutions efficiently. The shapes of all facilities were, however, assumed to be square. This paper proposes a facility layout method using Evolution Strategies for the case of different shapes and areas of facilities. Some numerical experiments made it clear that the proposed method provides solutions whose average relative error to the optimum or near-optimum solutions obtained by CPLEX are less than 2%, reducing computation time drastically.

A Heuristic Method for Minimizing Makespan in M-Stage Hybrid Flowshop

2012 ◽  
Author(s):  
Kazuko Morizawa ◽  
Naoki Hirabayashi
Keyword(s):  
Numerical Experiments ◽  
Parallel Machines ◽  
Heuristic Method ◽  
Computation Time ◽  
Second Phase ◽  
Scheduling Problem ◽  
Unrelated Parallel Machines ◽  
Two Phase ◽  
Hybrid Flowshop ◽  
Optimum Schedule

This paper deals with a scheduling problem to minimize makespan in m-stage hybrid flowshop with unrelated parallel-machines at least one stage. Since the problem is known to be NP-hard, a two-phase heuristic algorithm is proposed to obtain a near-optimum schedule efficiently. In the first phase of the proposed algorithm, some promising schedules with an identical job-sequence to all stages are generated by applying NEH algorithm in various ways, and then search better schedules by applying some heuristic job-moving strategies to these schedules in the second phase. Numerical experiments are implemented to demonstrate that the proposed method can provide a near-optimum schedule within a reasonable computation time.

scholarly journals Weighted Time-Band Approximation Model for Flight Operations Recovery considering Simplex Group Cycle Approaches in China

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Haiwen Xu ◽  
Songchen Han
Keyword(s):  
Numerical Experiments ◽  
Recovery Period ◽  
Computation Time ◽  
Actual Data ◽  
Approximation Model ◽  
Hub And Spoke ◽  
Control Center ◽  
Flight Operations ◽  
Operations Control ◽  
Time Band

The time-band approximation model for flight operations recovery following disruption (Bard, Yu, Arguello, IIE Transactions, 33, 931–947, 2001) is constructed by partitioning the recovery period into time bands and by approximating the delay costs associated with the possible flight connections. However, for disruptions occurring in a hub-and-spoke network, a large number of possible flight connections are constructed throughout the entire flight schedule, so as to obtain the approximate optimal. In this paper, we show the application of the simplex group cycle approach to hub-and-spoke airlines in China, along with the related weighted threshold necessary for controlling the computation time and the flight disruption scope and depth. Subsequently, we present the weighted time-band approximation model for flight operations recovery, which incorporates the simplex group cycle approach. Simple numerical experiments using actual data from Air China show that the weighted time-band approximation model is feasible, and the results of stochastic experiments using actual data from Sichuan Airlines show that the flight disruption and computation time are controlled by the airline operations control center, which aims to achieve a balance between the flight disruption scope and depth, computation time, and recovery value.

scholarly journals A Computational Method for Subdivision Depth of Ternary Schemes

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 817
Author(s):  
Faheem Khan ◽  
Ghulam Mustafa ◽  
Aamir Shahzad ◽  
Dumitru Baleanu ◽  
Maysaa M. Al-Qurashi
Keyword(s):  
Error Bounds ◽  
Numerical Experiments ◽  
Computational Method ◽  
Subdivision Schemes ◽  
Practical Applications ◽  
Refinement Procedure ◽  
Subdivision Algorithm ◽  
Subdivision Depth ◽  
Error Distance ◽  
New Framework

Subdivision schemes are extensively used in scientific and practical applications to produce continuous shapes in an iterative way. This paper introduces a framework to compute subdivision depths of ternary schemes. We first use subdivision algorithm in terms of convolution to compute the error bounds between two successive polygons produced by refinement procedure of subdivision schemes. Then, a formula for computing bound between the polygon at k-th stage and the limiting polygon is derived. After that, we predict numerically the number of subdivision steps (depths) required for smooth limiting shape based on the demand of user specified error (distance) tolerance. In addition, extensive numerical experiments were carried out to check the numerical outcomes of this new framework. The proposed methods are more efficient than the method proposed by Song et al.

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