• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.11
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• pp.4355-4371
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• 2020

Phase retrieval, recovering a signal from phaseless measurements, is generally considered to be an NP-hard problem. This paper adopts an amplitude-based nonconvex optimization cost function to develop a new stochastic gradient algorithm, named stochastic reweighted phase retrieval (SRPR). SRPR is a stochastic gradient iteration algorithm, which runs in two stages: First, we use a truncated sample stochastic variance reduction algorithm to initialize the objective function. The second stage is the gradient refinement stage, which uses continuous updating of the amplitude-based stochastic weighted gradient algorithm to improve the initial estimate. Because of the stochastic method, each iteration of the two stages of SRPR involves only one equation. Therefore, SRPR is simple, scalable, and fast. Compared with the state-of-the-art phase retrieval algorithm, simulation results show that SRPR has a faster convergence speed and fewer magnitude-only measurements required to reconstruct the signal, under the real- or complex- cases.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.665-678
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• 2022

The aim of this paper is to introduce a new iterative process and show that our iteration scheme is faster than other existing iteration schemes with the help of numerical examples. Next, we have established convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some convergence results for the approximation of the fixed points of a nonexpansive mapping.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.459-465
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• 2022

We exhibit various properties of the weighted Berezin operator T_α and its iteration T^k_α on L^p(𝜏), where α > -1 and 𝜏 is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(𝜏) the space of radial integrable functions have performed important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. We show differences between the case of 1 < p < ∞ and p = 1, ∞ under the infinite iteration of T_α or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.205-229
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• 2022

The aim of this paper is to obtain some results which belong to fixed point theory such as strong convergence, rate of convergence, stability, and data dependence by using the new Jungck-type iteration method for a mapping defined in complex-valued Banach spaces. In addition, some of these results are supported by nontrivial numerical examples. Finally, it is shown that the sequence obtained from the new iteration method converges to the solution of the functional integral equation in complex-valued Banach spaces. The results obtained in this paper may be interpreted as a generalization and improvement of the previously known results.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.303-313
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• 2023

Generalized strictly diagonally dominant matrices have a wide range of applications in matrix theory and practical applications, so it is of great theoretical and practical value to study their numerical determination methods. In this paper, we study the numerical determination of generalized strictly diagonally dominant matrices by using the properties of generalized strictly diagonally dominant matrices. We obtain a new criterion for subdivision iteration determination of the generalized strictly diagonally dominant matrices by subdividing the set of non-prevailing row indices and constructing new iteration factors for the set of predominant row indices, new elements of the positive diagonal factors are derived. Advantages are illustrated by numerical examples.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.141-154
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• 2024

This article offers a thorough exploration of a modified Black-Scholes model featuring two assets. The determination of option prices is accomplished through the Black-Scholes partial differential equation, leveraging the variational iteration method. This approach represents a semi-analytical technique that incorporates the use of Lagrange multipliers. The Lagrange multiplier emerges as a beacon of efficiency, adeptly streamlining the computational intricacies, and elevating the model's efficacy to unprecedented heights. For better understanding of the presented system, a graphical and tabular interpretation is presented with the help of Maple software.

• Journal of Korea Water Resources Association
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• v.53 no.5
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• pp.347-356
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• 2020

The main objective of the study is to propose the most efficient SWAT model calibration method using SWAT-CUP with less computing time and high performance. In order to achieve the goal, Case1-3 (250, 500, and 1,000 simulation runs) and Case4 (1,000 simulation runs in the first iteration and then 500 simulation runs for the following iterations) were defined to compare the results. When evaluating the values of the objective function, Case2 and Case3 reached the same value after the fourth iteration, and Case1 reached the closed value of Case2-3 after the eighth iteration. However, the final estimates of the parameters had different ranges in Cases1-3, and only the results of Case3 and Case4 converged similarly. Thus, it can be considered that the parameter calibration results are highly affected by the initial number of simulation runs. On the other hand, SWAT simulation results did not show the significant difference after the first iteration, unlike the parameter ranges. From the analysis results, we can conclude that the most suitable and effective method was to repeat one or two times of iterations with a sufficient number of simulation runs, as in Case4.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.329-337
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• 2007

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1275-1284
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• 2001

In this paper, we introduce an iteration generated by countable nonexpansive mappings and prove a weak convergence theorem which is connected with the feasibility problem. This result is used to solve the problem of finding a solution of the countable convex inequality system and the problem of finding a common fixed point for a commuting countable family of nonexpansive mappings.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.669-676
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• 2012

In this note we extend one well-known iteration formula to derive new third-order methods for solving a nonlinear equation. The comparison with other methods is given.