In this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unkno...
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In this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline v(h) defined by its values v(i) = v(h) (t(i)) at grid points (t)(i), i = 0, 1,..., N. The necessary for construction the cubic spline and missing the first derivatives at the boundary are replaced by the derivatives of the corresponding interpolating polynomials matching the grid points values nearest to the boundary points. An approximation of the solution is obtained by minimization techniques applied to a function whose arguments are the grid point values of the sought spline. The results of numerical experiments with two boundary value problems for the second order singularly perturbed delay differential equations as well as their comparison with the results of other methods employed by other authors are also provided.
Measuring the initial velocity is difficult in some enzyme assays where a significant fraction of the substrate is consumed. Here a solution to this problem is proposed;the time to produce a fixed amount of reaction p...
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Measuring the initial velocity is difficult in some enzyme assays where a significant fraction of the substrate is consumed. Here a solution to this problem is proposed;the time to produce a fixed amount of reaction product is measured. This time is inversely proportional to the initial velocity, and is related to the maximum velocity and Michaelis constant by a simple equation and linear plot. The method is illustrated using the reaction catalysed by pyruvate kinase.
Purpose - The purpose of this paper is to propose the speed-up of the fixed-point method by updating the reluctivity at each iteration (this is called a modified fixed-point method). Design/methodology/approach - A mo...
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Purpose - The purpose of this paper is to propose the speed-up of the fixed-point method by updating the reluctivity at each iteration (this is called a modified fixed-point method). Design/methodology/approach - A modified fixed-point method, which updates the derivative of reluctivity at each iteration, is proposed. It is shown that the formulation of the fixed-point method using the derivative of reluctivity is almost the same as that of the Newton-Raphson method. The convergence characteristic of the newly proposed fixed-point method is compared with those of the Newton-Raphson method. Findings - The modified fixed-point method has an advantage that the programming is easy and it has a similar convergence property to the Newton-Raphson method for an isotropic nonlinear problem. Originality/value - This paper presents the formulation and convergence characteristic of the modified fixed-point method are almost the same as those of the Newton-Raphson method.
In this paper, we first propose a new TVL2 regularization model for image restoration, and then we propose two iterative methods, which are fixed-point and fixed-point-like methods, using CGLS (Conjugate Gradient Leas...
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In this paper, we first propose a new TVL2 regularization model for image restoration, and then we propose two iterative methods, which are fixed-point and fixed-point-like methods, using CGLS (Conjugate Gradient Least Squares method) for solving the new proposed TVL2 problem. We also provide convergence analysis for the fixed-point method. Lastly, numerical experiments for several test problems are provided to evaluate the effectiveness of the proposed two iterative methods. Numerical results show that the new proposed TVL2 model is preferred over an existing TVL2 model and the proposed fixed-point-like method is well suited for the new TVL2 model.
Park (J. Math. Phys. 47: 103512, 2006) proved the Hyers-Ulam stability of homomorphisms in C*-ternary algebras and of derivations on C*-ternary algebras for the following generalized Cauchy-Jensen additive mapping: 2f...
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Park (J. Math. Phys. 47: 103512, 2006) proved the Hyers-Ulam stability of homomorphisms in C*-ternary algebras and of derivations on C*-ternary algebras for the following generalized Cauchy-Jensen additive mapping: 2f(Sigma(p)(j=1) X-j/2 + Sigma(d)(j=1)y(j)) = Sigma(p)(j=1) f(x(j)) + 2 Sigma(d)(j=1) f(y(j)). In this paper, we improve and generalize some results concerning this functional equation via the fixed-point method.
PurposeIn this paper, the authors study the nonlinear matrix equation Xp=Q +/- A(X-1+B)(-1)A(T), that occurs in many applications such as in filtering, network systems, optimal control and control ***/methodology/appr...
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PurposeIn this paper, the authors study the nonlinear matrix equation Xp=Q +/- A(X-1+B)(-1)A(T), that occurs in many applications such as in filtering, network systems, optimal control and control ***/methodology/approachThe authors present some theoretical results for the existence of the solution of this nonlinear matrix equation. Then the authors propose two iterative schemes without inversion to find the solution to the nonlinear matrix equation based on Newton's method and fixed-point iteration. Also the authors show that the proposed iterative schemes converge to the solution of the nonlinear matrix equation, under *** The efficiency indices of the proposed schemes are presented, and since the initial guesses of the proposed iterative schemes have a high cost, the authors reduce their cost by changing them. Therefore, compared to the previous scheme, the proposed schemes have superior efficiency ***/value Finally, the accuracy and effectiveness of the proposed schemes in comparison to an existing scheme are demonstrated by various numerical examples. Moreover, as an application, by using the proposed schemes, the authors can get the optimal controller state feedback of $x(t+1) = A x(t) + C v(t)$.
In this paper, we propose a fixed-point augmented Lagrangian method (FPALM) for general convex problems arising in image processing. We can easily obtain the alternating minimization algorithm (AMA) referred to [1] fr...
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In this paper, we propose a fixed-point augmented Lagrangian method (FPALM) for general convex problems arising in image processing. We can easily obtain the alternating minimization algorithm (AMA) referred to [1] from the proposed FPALM. The proof for the convergence of the FPALM is provided under some mild assumptions. We present two kinds of first-order augmented Lagrangian schemes and show their connections to first-order primal-dual algorithms [2]. Furthermore, we apply an acceleration rule to both the FPALM and AMA to achieve better convergence rates. Numerical examples on different image denosing models including the ROF model, the vectorial TVmodel, high order models and the TV-L-1 model are provided to demonstrate the efficiency of the proposed algorithms. (C) 2013 Elsevier Inc. All rights reserved.
We study a nonlinear psi-Hilfer fractional-order delay integro-differentialequation (psi-Hilfer FrODIDE) that incorporatesN-multiple variable timedelays. Utilizing the psi-Hilfer fractional derivative (psi-Hilfer-FrD)...
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We study a nonlinear psi-Hilfer fractional-order delay integro-differentialequation (psi-Hilfer FrODIDE) that incorporatesN-multiple variable timedelays. Utilizing the psi-Hilfer fractional derivative (psi-Hilfer-FrD), we inves-tigate the Ulam-Hyers--Rassias (U-H-R), semi-Ulam-Hyers-Rassias (semi-U-H-R) and Ulam-Hyers (U-H) stability of the considered psi-Hilfer FrO-DIDE through the fixed-point method. Throughout this work, using Banach'sfixed-point theorem and the Bielecki norm, we establish three new theoremsrelated to these qualitative concepts. The theorems presented in this work arenovel and contribute to the existing literature on the Ulam-type stability of psi-Hilfer FrODIDEs
In this paper, the even order tensor square root problem with Einstein product was investigated. The existence of structure-preserving square root of even order M-tensor was studied. Two fixed-point iteration methods ...
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In this paper, the even order tensor square root problem with Einstein product was investigated. The existence of structure-preserving square root of even order M-tensor was studied. Two fixed-point iteration methods were proposed to solve the tensor square root problem. Both of the two methods were easy to calculate and make use of tensor computations directly. Finally, two numerical examples were showed to verify the validity of the proposed fixed-point iteration methods.
The objective of this paper is to analyze a coupled problem that describes the propagation of the electric wave in the heart. The problem comprises coupled partial differential equations posed on a three-dimensional d...
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The objective of this paper is to analyze a coupled problem that describes the propagation of the electric wave in the heart. The problem comprises coupled partial differential equations posed on a three-dimensional domain representing the heart and on a one-dimensional tree representing the Purkinje network. Each system of PDEs is itself coupled to ordinary differential equations that describe the electrical activity at the cellular level. We establish the existence of a unique solution, utilizing a fixed-point approach with a judicious and non-conventional choice of functional spaces and contraction.
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