New methods for determining speciality of linear systems based at fat points in Pn

2013 ◽  
Vol 217 (5) ◽  
pp. 927-945 ◽  
Author(s):  
Stepan Paul
Keyword(s):  
Linear Systems ◽  
Fat Points ◽  
New Methods

SOR-like Methods with Optimization Model for Augmented Linear Systems

2017 ◽  
Vol 7 (1) ◽  
pp. 101-115 ◽  
Author(s):  
Rui-Ping Wen ◽  
Su-Dan Li ◽  
Guo-Yan Meng
Keyword(s):  
Linear Systems ◽  
Linear Equations ◽  
Optimization Technique ◽  
Relaxation Parameter ◽  
Convergence Theory ◽  
Optimization Models ◽  
System Of Linear Equations ◽  
Augmented System ◽  
New Methods ◽  
Outstanding Work

AbstractThere has been a lot of study on the SOR-like methods for solving the augmented system of linear equations since the outstanding work of Golub, Wu and Yuan (BIT 41(2001)71-85) was presented fifteen years ago. Based on the SOR-like methods, we establish a class of accelerated SOR-like methods for large sparse augmented linear systems by making use of optimization technique, which will find the optimal relaxation parameter ω by optimization models. We demonstrate the convergence theory of the new methods under suitable restrictions. The numerical examples show these methods are effective.

Pole-Placement for Multi-Input Linear Systems by State Feedback or State-Derivative Feedback

2012 ◽  
Vol 605-607 ◽  
pp. 1765-1768
Author(s):  
Zun Hai Gao ◽  
Xi Chen Ye
Keyword(s):  
Linear Systems ◽  
General Expression ◽  
State Feedback ◽  
Pole Placement ◽  
Arbitrary Parameter ◽  
Canonical Forms ◽  
Input System ◽  
New Methods

Generalized Wonham controllable canonical forms are introduced to apply to pole placement of state feedback or state derivative feedback. New methods of pole placement of both state feedback and state derivative feedback for multi-input system are proposed. The theory and approach are introduced, and the general expression gain matrices containing arbitrary parameter are obtained for both state feedback and state derivative feedback of the multi-input system.

Experiments with iterative methods for linear systems using GeoGebra and TI-Nspire

1970 ◽  
Vol 11 ◽  
pp. 89-102
Author(s):  
Gregor Milicic ◽  
Simon Plangg
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Stem Education ◽  
Approximate Solutions ◽  
New Methods ◽  
Dynamical Aspect ◽  
Key Topics ◽  
Algorithmic Thinking ◽  
Unsolvable Problems

Algorithms and algorithmic thinking are key topics in STEM Education. By using algorithms approximate solutions can be obtained for analytical unsolvable problems. Before new methods can be safely applied they have to be thoroughly tested in experiments. In this article we present a series of exercise where students can experiment with algorithms and test them using GeoGebra or the TI-Nspire. Based on the results of such experiments the students can compare algorithms, showing them a heuristic and dynamical aspect of Mathematics.

scholarly journals Modular Analysis of Sequential Solution Methods for Almost Block Diagonal Systems of Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Tarek M. A. El-Mistikawy
Keyword(s):  
Linear Systems ◽  
Systems Of Equations ◽  
New Methods ◽  
Partial Pivoting ◽  
Sequential Solution ◽  
Solution Methods ◽  
Modular Analysis ◽  
Linear Systems Of Equations ◽  
Block Diagonal

Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods. It also allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. The outcome of the analysis and implementation is to discover new methods that outperform a well-known method, a modification of which is, therefore, advocated.

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