Two Iterative Methods for Solving Linear Interval Systems

Siahlooei, Esmaeil; Fazeli, Seyed Abolfazl Shahzadeh

doi:10.1155/2018/2797038

Cited by 7 publications

(3 citation statements)

References 38 publications

(46 reference statements)

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“…Solving system of linear equations is a critical problem in linear algebra. e study in [16] presents iterative methods for solving a linear interval system of equations, which is a linear system involving uncertain coefficients appearing as interval numbers. e first method replaces real operations with interval operations based on the conjugate gradient method.…”

Section: Related Workmentioning

confidence: 99%

Some Criteria of the Knowledge Representation Method for an Intelligent Problem Solver in STEM Education

Nguyen

Nhon

Tran

et al. 2020

Applied Computational Intelligence and Soft Computing

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Nowadays, building intelligent systems for science, technology, engineering, and math (STEM) education is necessary to support the studying of learners. Intelligent problem solver (IPS) is a system that can be able to solve or tutor how to solve the problems automatically. Learners only declare hypothesis and goal of problems based on a sufficient specification language. They can request the program to solve it automatically or to give instructions that help them to solve it themselves. Knowledge representation plays a vital role in these kinds of intelligent systems. There are various methods for knowledge representation; however, they do not meet the requirements of an IPS in STEM education. In this paper, we propose the criteria of a knowledge model for an IPS in education. These criteria orient to develop a method for knowledge representation to meet actual requirements in practice, especially pedagogical requirements. For proving the effectiveness of these criteria, a knowledge model is also constructed. This model can satisfy these criteria and be applied to build IPS for courses, such as mathematics and physics.

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Section: Related Workmentioning

confidence: 99%

Some Criteria of the Knowledge Representation Method for an Intelligent Problem Solver in STEM Education

Nguyen

Nhon

Tran

et al. 2020

Applied Computational Intelligence and Soft Computing

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“…Scientists are aware of the shortcomings of the existing types of 1D-IA and are trying to develop new, more perfect versions. For example, Siahlooei and Shahzadeh Fazeli (2018) propose IA based on new inverse operations of addition and multiplication and a new concept of the general closed interval.…”

Section: Introductionmentioning

confidence: 99%

A realistic tolerant solution of a system of interval linear equations with the use of multidimensional interval arithmetic

Piegat,

Pluciński

2023

International Journal of Applied Mathematics and Computer Scien

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The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors' previously published method for first-order ILEs.

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“…Numerous authors, including Alefeld et al [8], Beaumont [9], Siahlooei [10], Hansen [11,12], Sainz et al [13],…”

Section: Introductionmentioning

confidence: 99%

Implementing Interval Linear Equations Systems for Enhanced Circuit Analysis

Subramanian,

Thamaraiselvan,

Kandasamy

2023

MMEP

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The present study is centered around the deployment of interval linear equations systems in circuit analysis. In the domain of circuit theory, each circuit, constituted by components such as resistance, inductance, and capacitance, can be mathematically represented as a system of linear equations. In the context of electrical circuits, interval representations of current or voltage are considered more informative than single precise values. This is attributed to factors including fluctuating environmental conditions, current variations, tolerances in electrical elements, and power harmonic leakage. The integration of interval linear equations systems becomes crucial in accommodating these variables. We propose an algorithm using a new type of arithmetic operations and pairing technique on intervals for the interval solution of interval linear equations systems. We provide a numerical example to highlight the usefulness of the suggested approach. We also discuss an electrical circuit problem under an uncertain environment by using the proposed algorithm and interval arithmetic operations.

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Two Iterative Methods for Solving Linear Interval Systems

Cited by 7 publications

References 38 publications

Some Criteria of the Knowledge Representation Method for an Intelligent Problem Solver in STEM Education

Some Criteria of the Knowledge Representation Method for an Intelligent Problem Solver in STEM Education

A realistic tolerant solution of a system of interval linear equations with the use of multidimensional interval arithmetic

Implementing Interval Linear Equations Systems for Enhanced Circuit Analysis

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