CMES-Vol. 97, No. 2, 2014

Open Access

ARTICLE

Novel Iterative Algorithms Based on Regularization Total Least Squares for Solving the Numerical Solution of Discrete Fredholm Integral Equation
Zichun Yang^1,2,3, Lei Zhang^1,4, Yueyun Cao¹
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 101-130, 2014, DOI:10.3970/cmes.2014.097.101
Abstract Discretization of inverse problems often leads to systems of linear equations with a highly ill-conditioned coefficient matrix. To find meaningful solutions of such systems, one kind of prevailing and representative approaches is the so-called regularized total least squares (TLS) method when both the system matrix and the observation term are contaminated by some noises. We will survey two such regularization methods in the TLS setting. One is the iterative truncated TLS (TTLS) method which can solve a convergent sequence of projected linear systems generated by Lanczos bidiagonalization. The other one is to convert the Tikhonov… More >

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ARTICLE

Frequency Domain Based Solution for Certain Class of Wave Equations: An exhaustive study of Numerical Solutions
Vinita Chellappan¹, S. Gopalakrishnan¹ and V. Mani¹
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 131-174, 2014, DOI:10.3970/cmes.2014.097.131
Abstract The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly… More >

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ARTICLE

Enrichment Procedures for Soft Clusters: A Statistical Test and its Applications
R.D. Phillips¹, M.S. Hossain¹, L.T. Watson^1,2, R.H. Wynne³, Naren Ramakrishnan¹
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 175-197, 2014, DOI:10.3970/cmes.2014.097.175
Abstract Clusters, typically mined by modeling locality of attribute spaces, are often evaluated for their ability to demonstrate ‘enrichment’ of categorical features. A cluster enrichment procedure evaluates the membership of a cluster for significant representation in predefined categories of interest. While classical enrichment procedures assume a hard clustering definition, this paper introduces a new statistical test that computes enrichments for soft clusters. Application of the new test to several scientific datasets is given. More >

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