. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Chapter

In many applications one is interested in finding solutions to nonlinear evolution equations with a particular spatial and temporal structure. For instance, solitons in optical fibers and wave guides or buckling modes of long structures can be interpreted as localised travelling or standing waves of an appropriate underlying partial differential equation (PDE) posed on an unbounded domain. Spir...

In this paper we deal with the problem of numerical computation of Gröbner bases of zero-dimensional polynomial systems. It is well known that the computation of a Gröbner basis cannot be generally executed in floating-point arithmetic by a standard approach. This, however, would be highly desirable for practical applications. We present an approach for computing Gröbner bases numerically. It i...

This symposium explores the role of placeholder structures—systems of words, non-linguistic symbols, or procedures—in the construction and manipulation of numerical concepts. The structure supplied by a placeholder system – like the count list in English – critically constrains the potential for creating and manipulating conceptual content. A great deal of empirical work has explored the role o...

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In this paper, an algorithm based on the Drazin generalized conjugate residual (DGMRES) algorithm is proposed for computing the group-inverse solution of singular linear equations with index one. Numerical experiments show that the resulting group-inverse solution is reasonably accurate and its computation time is significantly less than that of group-inverse solution obtained by the DGMRES alg...

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...