• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.182-188
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• 1991

The modified arc-length algorithms for the automatic incremental solution of nonlinear finite element equations proposed by Riks are presented, which comprise the cylindrical arc-length method and the normal arc-length method. These methods are developed to trace the nonlinear path of large displacement problems such as a pre and post bucking/collapse response of general structures. These methods are applied to analyse the nonlinear behavior of arch and shell problems in parallel with the standard and modified Newton-Raphson method.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.47-55
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• 2008

Local convergence results for three Newton-like methods in Banach space are provided. A comparison is given between the three convergence radii. Then we show that using the largest convergence radius we can pick an initial guess from with we start the corresponding iteration. It turns out that after a finite number of steps we can always use the iterate found as the starting guess for a faster method, since this iterate will be inside the convergence domain of the new method.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.311-319
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• 2007

This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation $B_k+1{^s}_k=yk\;where\;y_k^*=yk+A_ks_k\;and\;A_k$ is a matrix. Wei, Li and Qi [WLQ] have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule.

• Computational Structural Engineering
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• v.11 no.1
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• pp.205-216
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• 1998

A solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of nonclassicary damped structural systems with multiple eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem through matrix augmentation of the quadratic eigenvalue problem. In the iteration methods such as the inverse iteration method and the subspace iteration method, singularity may be occurred during the factorizing process when the shift value is close to an eigenvalue of the system. However, even though the shift value is an eigenvalue of the system, the proposed method provides nonsingularity, and that is analytically proved. Since the modified Newton-Raphson technique is adopted to the proposed method, initial values are need. Because the Lanczos method effectively produces better initial values than other methods, the results of the Lanczos method are taken as the initial values of the proposed method. Two numerical examples are presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well-known subspace iteration method and the Lanczos method.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.279-282
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• 2007

Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.195-205
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• 2004

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

• East Asian mathematical journal
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• v.23 no.2
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• pp.257-260
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• 2007

Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].

• Journal of Powder Materials
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• v.29 no.4
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• pp.303-308
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• 2022

The plastic deformation behavior of additively manufactured anisotropic structures are analyzed using the finite element method (FEM). Hill's quadratic anisotropic yield function is used, and a modified return-mapping method based on dual potential is presented. The plane stress biaxial loading condition is considered to investigate the number of iterations required for the convergence of the Newton-Raphson method during plastic deformation analysis. In this study, incompressible plastic deformation is considered, and the associated flow rule is assumed. The modified return-mapping method is implemented using the ABAQUS UMAT subroutine and effective in reducing the number of iterations in the Newton-Raphson method. The anisotropic tensile behavior is computed using the 3-dimensional FEM for two tensile specimens manufactured along orthogonal additive directions.

• Journal of IKEEE
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• v.19 no.2
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• pp.219-224
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• 2015

Electrical impedance tomography is an imaging technique to reconstruct the internal conductivity distribution based on applied currents and measured voltages in a domain of interest. In this paper, a modified Gauss-Newton method is proposed for conductivity image reconstruction. In the proposed method, the dimension of the inverse term is reduced by replacing the number of elements with the number of measurement data in the conductivity updating equation of the conventional Gauss-Newton method. Therefore, the computation time is greatly reduced as compared to the conventional Gauss-Newton method. Moreover, the regularization parameter is selected by computing the minimum-maximum from the diagonal components of the Jacobian matrix at every iteration. The numerical experiments with several scenarios were carried out to evaluate the reconstruction performance of the proposed method.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.6
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• pp.34-44
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• 1994

In this paper, an iterative inversion method in angular spectral domain is presented for microwave imaging of a perfectly conducting cylinder. Angular spectra are calculated from measured far-field scattered fields. And then both the propagating modes and the evanescent modes are defined. The center and initial shape of an unknown conductor may be obtained by the characteristics of angular spectra and the total scattering cross section (TSCS). Finally, the orignal shape is reconstructed by the modified Newton algorithm. By using well estimated initial shape the local minima can be avoided, which might appear when the nonlinear equation is solved with Newton algorithm. It is shown to be robust to noise in scattered fields via numerical examples by keeping only the propagating modes and filtering out the evanescent modes.