a 'sleeper', receiving only modest attention for 50 years before emerging as a cornerstone of communications engineering in more recent times. Roughly one in six of Walsh's 281 publications are included, photographically reproduced. Reproduction is excellent except for one paper from 1918. The book also reproduces three brief papers about Walsh and his work, by W. E. Sewell, D. V. Widder and Morris Marden. The first two were written for a special issue of the SIAM Journal celebrating Walsh's 70th birthday; the third is an obituary.

Matrix iterative analysis (2nd edn), by Richard S. Varga. Springer Series in Computational Mathematics 27. Pp. 358. £55. 2000. ISBN 3 540 66321 5 (Springer Verlag).

Optimization can be defined as an effort of generating solutions to a problem under bounded circumstances. Optimization methods have arisen from a desire to utilize existing resources in the best possible way. An important class of optimization methods is heuristic algorithms. Heuristic algorithms have generally been proposed by inspiration from the nature. For instance, Particle Swarm Optimization has been inspired by social behavior patterns of fish schooling or bird flocking. Bat algorithm is a heuristic algorithm proposed by Yang in 2010 and has been inspired by a property, named as echolocation, which guides the bats' movements during their flight and hunting even in complete darkness. In this work, local and global search characteristics of bat algorithm have been enhanced through three different methods. To validate the performance of the Enhanced Bat Algorithm (EBA), standard test functions and constrained real-world problems have been employed. The results obtained by these test sets have proven EBA superior to the standard one. Furthermore, the method proposed in this study is compared with recently published studies in the literature on real-world problems and it is proven that this method is more effective than the studies belonging to other literature on this sort of problems.

A new modification approach on bat algorithm for solving optimization problems

This paper is concerned with solving some structured multi-linear systems, especially focusing on the equations whose coefficient tensors are $$\mathcal {M}$$M-tensors, or called $$\mathcal {M}$$M-equations for short. We prove that a nonsingular $$\mathcal {M}$$M-equation with a positive right-hand side always has a unique positive solution. Several iterative algorithms are proposed for solving multi-linear nonsingular $$\mathcal {M}$$M-equations, generalizing the classical iterative methods and the Newton method for linear systems. Furthermore, we apply the $$\mathcal {M}$$M-equations to some nonlinear differential equations and the inverse iteration for spectral radii of nonnegative tensors.

Solving Multi-linear Systems with $$\mathcal {M}$$M-Tensors

A new eigenvalue localization set for tensors is given, and proved to be tighter than those in [Qi L. Eigenvalues of a real supersymmetric tensor. J. Symbolic Comput. 2005;40:1302–1324] and [Li CQ, Li YT, Kong X. New eigenvalue inclusion sets for tensors. Numer. Linear Algebra Appl. 2014;21:39–50]. Based on this set, we give two checkable sufficient conditions of the positive definiteness of tensors, and two checkable sufficient conditions of the positive semi-definiteness of tensors.

An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors

An H-tensor based iterative scheme for identifying the positive definiteness of multivariate homogeneous forms

Criterions for the positive definiteness of real supersymmetric tensors

Several new criteria for identifying -tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. Advantages of the obtained results are illustrated by numerical examples.

New practical criteria for ℋ-tensors and its application

Some new preconditioned GAOR methods for solving generalized least-squares problems and their comparison results are given. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods presented by Shen et al. [Preconditioned iterative methods for solving weighted linear least squares problems, Appl. Math. Mech. – Engl. Ed. 33(3) (2012), pp. 375–384] whenever these methods are convergent. Lastly, numerical experiments are provided to confirm the theoretical results.

Some new preconditioned generalized AOR methods for generalized least-squares problems

In this paper, new error bounds for the linear complementarity problem are obtained when the involved matrix is a weakly chained diagonally dominant B-matrix. The proposed error bounds are better than some existing results. The advantages of the results obtained are illustrated by numerical examples.

/pdf/error-bounds-for-linear-complementarity-problems-of-weakly-1suulxyn2l.pdf

Error bounds for linear complementarity problems of weakly chained diagonally dominant B-matrices.

A new error bound for the linear complementarity problem is obtained when the involved matrix is a B-matrix. This bound improves existing results. Finally, two numerical examples are also g...

New error bound for linear complementarity problems for B-matrices

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