Solving systems of linear functional equations with computer

Borus, Gergő Gyula; Gilányi, Attila

doi:10.1109/coginfocom.2013.6719310

Cited by 19 publications

(4 citation statements)

References 15 publications

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“…The results of one further research let us complete our typology, namely research in mathability [19] [20] [21] [22]. According to the authors, they apply the concept of mathability to the usage of computer tools.…”

Section: The Mathability Of Computer Problem Solving Approachesmentioning

confidence: 99%

Thinking Fast and Slow in Computer Problem Solving

Csernoch¹

2017

JSEA

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Research in spreadsheet management proved that the overuse of slow thinking, rather than fast thinking, is the primary source of erroneous end-user computing. However, we found that the reality is not that simple. To view end-user computing in its full complexity, we launched a project to investigate end-user education, training, support, activities, and computer problem solving. In this project we also set up the base and mathability-extended typology of computer problem solving approaches, where quantitative values are assigned to the different problem solving methods and activities. In this paper we present the results of our analyses of teaching materials collected in different languages from all over the world and our findings considering the different problem solving approaches, set in the frame of different thinking modes, the characteristics of expert teachers, and the meaning system model of teaching approaches. Based on our research, we argue that the proportions of fast and slow thinking and most importantly their manifestation are responsible for erroneous end-user activities. Applying the five-point mathability scale of computer problem solving, we recognized slow thinking activities on both tails and one fast thinking approach between them. The low mathability slow thinking activities, where surface navigation and language details are focused on, are widely accepted in end-user computing. The high mathability slow thinking problem solving activities, where the utilization of concept based approaches and schema construction take place, is hardly detectable in end-user activities. Instead of building up knowledge which requires slow thinking and then using the tools with fast thinking, end-users use up their slow thinking in aimless wandering in huge programs, making wrong decisions based on their untrained, clueless intuition, and distributing erroneous end-user documents. We also found that the dominance of low mathability slow thinking activities has its roots in the education system and through this we point out that we are in great need of expert teachers and institutions and their widely accepted approaches and methods.

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Section: The Mathability Of Computer Problem Solving Approachesmentioning

confidence: 99%

Thinking Fast and Slow in Computer Problem Solving

Csernoch¹

2017

JSEA

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“…This is possible with the application of the option verbose. If we use this, the program presents the unknown functions in the system considered as sums of monomial functions (similarly to (7) and (10) in Theorems 1 and 2, respectively), it yields the connections between these monomials (solving the systems of equations ( 8) or ( 11)), finally, it also gives the solutions as above. The solutions of the square-norm equation (16) with this option will be presented in the following form:…”

Section: Description Of the Programmentioning

confidence: 99%

“…We note that a previous version of the program was presented during the 4 th IEEE International Conference on Cognitive Infocommunications (CogIn-foCom) in 2013 (cf. [10]) and also a related Demo Presentation was performed at the same conference (cf. [9]).…”

Section: Introductionmentioning

confidence: 99%

Computer assisted solution of systems of two variable linear functional equations

Borus

Gilányi

2020

Aequat. Math.

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“…Its solutions, in a general case, were determined by Székelyhidi [22,23]. A computer program presenting the solutions of functional equations of type (1) was described in [7] (cf., also, [5,6,10,11]). Problems connected to class (1), its generalizations and its applications have been studied by several authors during the last more than 100 years.…”

Section: Introductionmentioning

confidence: 99%

On linear functional equations modulo $${\mathbb {Z}}$$

Gilányi

Lewicka

2021

Aequat. Math.

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In this paper, we consider the condition $$\sum _{i=0}^{n+1}\varphi _i(r_ix+q_iy)\in {\mathbb {Z}}$$ ∑ i = 0 n + 1 φ i ( r i x + q i y ) ∈ Z for real valued functions defined on a linear space V. We derive necessary and sufficient conditions for functions satisfying this condition to be decent in the following sense: there exist functions $$f_i:V\rightarrow {\mathbb {R}}$$ f i : V → R , $$g_i:V\rightarrow {\mathbb {Z}}$$ g i : V → Z such that $$\varphi _i=f_i+g_i$$ φ i = f i + g i , $$(i=0,\dots ,n+1)$$ ( i = 0 , ⋯ , n + 1 ) and $$\sum _{i=0}^{n+1}f_i(r_ix+q_iy)=0$$ ∑ i = 0 n + 1 f i ( r i x + q i y ) = 0 for all $$x, y\in V$$ x , y ∈ V .

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Solving systems of linear functional equations with computer

Cited by 19 publications

References 15 publications

Thinking Fast and Slow in Computer Problem Solving

Thinking Fast and Slow in Computer Problem Solving

Computer assisted solution of systems of two variable linear functional equations

On linear functional equations modulo $${\mathbb {Z}}$$

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