• Journal of applied mathematics & informatics
• /
• v.4 no.1
• /
• pp.83-108
• /
• 1997

Chebysheff-Halley methods are probably the best known cubically convergent iterative procedures for solving nonlinear equa-tions. These methods however require an evaluation of the second Frechet-derivative at each step which means a number of function eval-uations proportional to the cube of the dimension of the space. To re-duce the computational cost we replace the second Frechet derivative with a fixed bounded bilinear operator. Using the majorant method and Newton-Kantorovich type hypotheses we provide sufficient condi-tions for the convergence of our method to a locally unique solution of a nonlinear equation in Banach space. Our method is shown to be faster than Newton's method under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.

• Computational Structural Engineering
• /
• v.7 no.4
• /
• pp.85-101
• /
• 1994

A family of variational principles governing the dynamics of laminated plate has been derived using a variationally consistent shear deformable discrete laminated plate theory with particular reference to finite element procedures. The theoretical basis for the derivation is Sandhu's generalized procedure for the variational formulation of linear coupled boundary value problem. As the bilinear mapping to write the operator matrix of the field equations in self-adjoint form, convolution product was employed. Boundary conditions, initial conditions and probable internal discontinuity were explicitly included in the governing functionals. Some interesting extensions and specializations of the general variational principle were presented, which can provide many different finite element formulations for the problem.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.50 no.9
• /
• pp.194-200
• /
• 2013

In this paper, we propose a multi-scale crack detection method using scaling. It is based on morphology algorithm, crack features, and scaling. We use a morphology operator which extracts patterns of crack. It segments cracks and background using opening and closing operations. Morphology based segmentation is better than existing integration methods using subtraction in detecting a crack it has small width. However, morphology methods using only one structure element could detect only fixed width crack. Thus, we use a scaling method. We use bilinear interpolation for scaling. Our method calculates values of properties such as the number of pixels and the maximum length of the segmented region. We decide whether the segmented region belongs to cracks according to those data. Experimental results show that our proposed multi-scale crack detection method has better results than those of existing detection methods.