Numerical linear algebra: Theory and applications

© Springer International Publishing AG 2017. All rights reserved. This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level

A multigrid method for weakly nonlinear elliptic equations of the second order

We consider the Dirichlet problem for a weakly nonlinear elliptic equation of the second order in the divergence form. We prove the convergence of a multigrid method for solving this problem. The method under consideration is based on the application of conformal finite elements and the Jacobi smoothing procedure. © 2011 Allerton Press, Inc

Reconstruction of dielectric constants of multi-layered optical fibers using propagation constants measurements

We present new method for the numerical reconstruction of the variable refractive index of multi-layered circular weakly guiding dielectric waveguides using the measurements of the propagation constants of their eigenwaves. Our numerical examples show stable reconstruction of the dielectric permittivity function $\varepsilon$ for random noise level using these measurements

Investigation of the solvability of the nonlinear equilibrium problem for an unfixed shallow shell

© 2014, Pleiades Publishing, Ltd. A sufficient condition for the solvability of the variational problem on the equilibrium of a shallow shell with free edges is obtained in the framework of a geometrically and physically nonlinear model of median bending

Investigation of the solvability of the nonlinear equilibrium problem for an unfixed shallow shell

© 2014, Pleiades Publishing, Ltd. A sufficient condition for the solvability of the variational problem on the equilibrium of a shallow shell with free edges is obtained in the framework of a geometrically and physically nonlinear model of median bending

Numerical linear algebra: Theory and applications

© Springer International Publishing AG 2017. All rights reserved. This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level

A multigrid method for weakly nonlinear elliptic equations of the second order

We consider the Dirichlet problem for a weakly nonlinear elliptic equation of the second order in the divergence form. We prove the convergence of a multigrid method for solving this problem. The method under consideration is based on the application of conformal finite elements and the Jacobi smoothing procedure. © 2011 Allerton Press, Inc

Investigation of the solvability of the nonlinear equilibrium problem for an unfixed shallow shell

© 2014, Pleiades Publishing, Ltd. A sufficient condition for the solvability of the variational problem on the equilibrium of a shallow shell with free edges is obtained in the framework of a geometrically and physically nonlinear model of median bending