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Local Convergence for a Fifth Order Traub-Steffensen-Chebyshev-Like Composition Free of Derivatives in Banach Space

Numerical Mathematics(Theory,Methods and Applications) 2018年第1期11卷 160-168页

作者： Ioannis K.Argyros santhosh george Department of Mathematical Sciences Cameron UniversityLawtonOK 73505USA Department of Mathematical and Computational Sciences NIT KarnatakaIndia 575025

We present the local convergence analysis of a fifth order Traub-Steffensen-Chebyshev-like composition for solving nonlinear equations in Banach *** earlier studies,hypotheses on the Fréchet derivative up to the fifth order of the operator un-der consideration is used to prove the convergence order of the method although only divided differences of order one appear in the *** restricts the applicability of the *** this paper,we extended the applicability of the fifth order Traub-Steffensen-Chebyshev-like composition without using hypotheses on the derivatives of the operator *** convergence conditions are weaker than the conditions used in earlier *** examples where earlier results cannot apply to solve equa-tions but our results can apply are also given in this study.

关键词： Traub-Steffensen-Chebyshev-like composition restricted convergence domain radius of convergence local convergence

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LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES

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Acta Mathematica Scientia 2018年第1期38卷 303-314页

作者： santhosh george C.D.SREEDEEP Department of Mathematical and Computational Sciences NIT Karnataka

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the imple- mentation of Lavrentiev regularization method. Using general HSlder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock （2005） for choosing the regularization parameter.

关键词： nonlinear ill-posed problem Banach space Lavrentiev regularization m-accretive mappings adaptive parameter choice strategy

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ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES

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Acta Mathematica Scientia 2015年第6期35卷 1318-1324页

作者： Ioannis K.ARGYROS santhosh george Department of Mathematical Sciences Cameron University Department of Mathematical and Computational Sciences National Institute of Technology Karnataka

In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.

关键词： nonlinear ill-posed equations iterative regularization m-accretive operator Newton type method

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LOCAL CONVERGENCE OF INEXACT NEWTON-LIKE METHOD UNDER WEAK LIPSCHITZ CONDITIONS

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Acta Mathematica Scientia 2020年第1期40卷 199-210页

作者： Ioannis KARGYROS Yeol Je CHO santhosh george Yibin XIAO Department of Mathematical Sciences Cameron UniversityLawtonOK 73505USA School of Mathematical Sciences University of Electronic Science and Technology of ChinaChengdu 611731China Department of Mathematics Education Gyeongsang National UniversityJinju 52828Korea Department of Mathematical and Computational Sciences National Institute of TechnologyKarnataka757025 India

The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space *** employ weak Lipschitz and center-weak Lipschitz conditions to perform the error *** obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.

关键词： inexact Newton method Banach space semilocal convergence weak and center-weak Lipschitz condition recurrent functions Kantorovich hypotheses

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Measurement of Elastic Parameters of Lithium Hydroxylammonium Sulphate Single Crystal, by Ultrasonic Pulse Echo Overlap Technique

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Open Journal of Acoustics 2014年第3期4卷 138-144页

作者： george Varughese santhosh Kumar Department of Physics Catholicate College Pathanamthitta India SPAP Mahatma Gandh University Kottayam India

Ultrasonics is the most established and precise technique to determine the elastic parameters of materials. Elastic constants are important parameters of a crystal which provide valuable infor-mation about the bonding characteristic between adjacent atomic planes and the anisotropic cha-racter of the bonding and structural ability. Second order elastic constants can be measured by measuring the velocity of the ultrasonic pulses of different polarization along different symmetry directions. Elastic Constants of Lithium Hydroxylammonium Sulphate [LHAS] single crystal by ul-trasonic Pulse Echo Overlap [PEO] technique are reported for the first time. Large single crystals of LHAS of size [26×26×10] ?mm3 have been grown from supersaturated aqueous solution of the salt by slow evaporation technique over a period of 40 - 45 days at 305 K. Absolute velocities at room temperature (303 K) have been measured for the selected direction and modes with McSkimin criterion. The anisotropy in the elastic properties of LHAS is well studied by measuring ultrasonic velocity in the crystal in certain specified crystallographic directions. The elastic stiffness constants C11, C33, C44, C55, and C66, and Acoustic impedance constants and Rao’s constants in specified directions are evaluated.

关键词： Inorganic Compounds Crystal Growth Ultrasonic Velocity Elastic Constants

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Ultrasonic Investigation of Elastic Anomalies in Lithium Sodium Sulphate Hexahydrate Single Crystal

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Open Journal of Acoustics 2014年第3期4卷 131-137页

作者： george Varughese santhosh Kumar Department of Physics Catholicate College Pathanamthitta India SPAP Mahatma Gandhi University Kottayam India

An extensive study of the thermal properties of Lithium Sodium Sulphate Hexa hydrate (LSSW) single crystal, with Trigonal structure, has been carried out using ultrasonic Pulse Echo Overlap (PEO) technique, Differential Thermal Analysis (DTA) and Thermo Gravimetric Analysis (TGA). The temperature variation of elastic constants of LiNa3(SO4)2·6H2O single crystal have been reported for the first time. The second order elastic stiffness constants C11,?C33, C44, along the various directions in the crystal have been determined in the temperature range 300 - 330 K. The change in velocity with temperature with respect to the room temperature value has been measured using PEO technique. Significant anomalies were observed in C11?and C33?at 316 K. The elastic constant C12?has shown no variation in the temperature range 300 - 319 K. A minor deviation for C44?at 305 K following a parabolic change has been observed. The minor anomalies observed in the elastic constants of LSSW may be due to its dehydration of water of crystallization in the range 304 - 319 K. DTA studies showed an appreciable endothermic change in the range 309 K-369.79 K. TGA curve exhibited a decrease in weight of 1.687 mg in the temperature range 304 K-360 K. The minor anomalies observed in the elastic constants of LSSW may be due to loosing of its water of crystallization in the range 309 - 319 K. On loosing water there will not be any change in chemical structure but there will be physical change associated with loosing of water molecule.

关键词： Ultrasonics Single Crystal Elastic Properties Pulse Echo Overlap Technique

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