In a computational program there can be two kinds of errors: (i) critical errors and (ii) non-critical errors. A critical error stops the program in a global way, which means the error cannot be fixed in the subsequen...
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In a computational program there can be two kinds of errors: (i) critical errors and (ii) non-critical errors. A critical error stops the program in a global way, which means the error cannot be fixed in the subsequent computation process. A non-critical error partially stops the computation program, and the error can be fixed in the subsequent computation process. We argue that two kinds of errors correspond to two kinds of suspension and can be modeled using ParaconsistentWeak Kleene (PWK) belief revision theory, with the help of a new interpretation of the third value of PWK, that is, off-topic. According to this new interpretation, if a proposition obtains the third value u, it means it is off-topic. Within our framework of PWK belief revision theory, we will show that a non-critical error corresponds to a non-critical suspension and that a critical error corresponds to a critical suspension.
Our aim in this paper is to study variants and computational errors of the extragradient method for solving equilibrium problems. First, we consider convergence of the method when domains in the auxiliary subproblems ...
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Our aim in this paper is to study variants and computational errors of the extragradient method for solving equilibrium problems. First, we consider convergence of the method when domains in the auxiliary subproblems of the extragradient algorithm are replaced by outer and inner approximation polyhedra. Then, computational errors are showed under the asymptotic optimality condition, but the bifunction must satisfy certain Lipschitz-type continuous conditions. Next, by using Armijo-type linesearch techniques commonly used in variational inequalities, we obtain an approximation linesearch algorithm without Lipschitz continuity. Convergence analysis of the algorithms is considered under mild conditions on the iterative parameters.
The finite-difference method is used for solving the diffusion equation of nuclear magnetization in discrete space and time. The purpose of this study was to obtain the time step Delta t and the spatial step Delta x, ...
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The finite-difference method is used for solving the diffusion equation of nuclear magnetization in discrete space and time. The purpose of this study was to obtain the time step Delta t and the spatial step Delta x, which minimize computational errors in simulation. We evaluated the difference between a discrete solution and an explicit solution that had been derived from the magnetization diffusion equation. The results revealed the existence of Delta x, which minimizes computational errors. The spatial step Delta x and computational errors increased as the time step Delta t increased. The results should be useful for efficiently carrying out diffusion simulations within given time limitations for computation.
A method is proposed for the estimation of computational errors in the fixed-step integration of nonlinear systems of differential equations. This method finds the bifurcation parameters from the characteristic values...
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A method is proposed for the estimation of computational errors in the fixed-step integration of nonlinear systems of differential equations. This method finds the bifurcation parameters from the characteristic values of the scheme-generated discrete set and then measures the deviation from expected values at well-defined bifurcation events. With the help of some nonlinear test models, it was found that this deviation or error obeys a scaling law function of the integration step with a characteristic noninteger exponent. Our results are in agreement with previously reported errors in first order schemes. The examination of bifurcation parameters as a function of both the step and initial conditions showed the presence of several attractors where a simpler dynamics was expected. Further considerations of shadowing effects and the presence of a limiting step size are consistent with a complex build up of computational error as manifested by the scaling law.
Approximate rules for evaluating linear functionals are often obtained by requiring that the rule shall give exact value for a certain linear class of functions. The parameters of the rule appear hence as the solution...
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This article uses the concurrent mixed methods design to explore the errors made by 171 Grade Seven learners in algebraic problem-solving within the Assin Central Municipality in Ghana. The participants were categoriz...
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This article uses the concurrent mixed methods design to explore the errors made by 171 Grade Seven learners in algebraic problem-solving within the Assin Central Municipality in Ghana. The participants were categorized into low-achieving and high-achieving groups based on their performance in a pretest, to help provide a detailed examination of the discrepancies in error occurrence between these groups. The Newman error analysis framework was used to unveil distinct patterns of errors among learners when tackling algebraic tasks. Quantitative data from the test were complemented by qualitative insights employing the Think Aloud Protocols (TAP). The analysis revealed that low-achieving learners struggled with reading, comprehension, and transformation errors, while high-achieving learners mainly encountered transformation and process skill errors. The findings contribute valuable insights into learners' challenges in mastering algebraic concepts, offering implications for educational interventions and curriculum development in mathematics education. The study recommends implementing differentiated instruction strategies and providing additional support for comprehension, and problem-solving skills to improve algebraic proficiency among learners.
This paper introduces an alternate approach to error control in residue number systems which utilizes sets of moduli that include pairs with non-trivial common factors. Necessary and sufficient conditions for achievin...
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This paper introduces an alternate approach to error control in residue number systems which utilizes sets of moduli that include pairs with non-trivial common factors. Necessary and sufficient conditions for achieving a specified capacity for error detection or correction are derived by considering the minimum Hamming distance of an associated linear code. Effective error-control procedures are developed based on a syndrome matrix whose entries are obtained directly from the residue digits. The potential of a priori bounds on the magnitude of measurement errors to increase the efficiency of the control process is analyzed.
The differences between the actual equations of molecular dynamics method (MD) and the Newtonian ones due to numerical integration errors are analyzed. Condition of total energy conservation in MD is obtained. The sim...
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The differences between the actual equations of molecular dynamics method (MD) and the Newtonian ones due to numerical integration errors are analyzed. Condition of total energy conservation in MD is obtained. The simplest schemes satisfying this condition and the total energy fluctuations in MD are considered. Statistical meaning of MD and possible analogies of the MD equations in real molecular systems are discussed.
This study shows a new way to implement terrain-following s-coordinate in a numerical model,which does not lead to the well-known"pressure gradient force(PGF)"***,the causes of the PGF problemare analyzedwit...
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This study shows a new way to implement terrain-following s-coordinate in a numerical model,which does not lead to the well-known"pressure gradient force(PGF)"***,the causes of the PGF problemare analyzedwith existing methods that are categorized into two different types based on the ***,the new method that bypasses the PGF problem all together is *** comparing these threemethods and analyzing the expression of the scalar gradient in a curvilinear coordinate system,this study finds out that only when using the covariant scalar equations of s-coordinate will the PGF computational form have one term in each momentum component equation,thereby avoiding the PGF problem completely.A convenient way of implementing the covariant scalar equations of s-coordinate in a numerical atmospheric model is illustrated,which is to set corresponding parameters in the scalar equations of the Cartesian ***,two idealized experimentsmanifest that the PGF calculated with the new method is more accurate than using the classic *** method can be used for oceanic models as well,and needs to be tested in both the atmospheric and oceanic models.
Software-intensive science (SIS) challenges in many ways our current scientific methods. This affects significantly our notion of science and scientific interpretation of the world, driving at the same time the philos...
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