Triangulation of Convex Polygon with Storage Support

Unlike the algorithms for convex polygon triangulation which make the triangulation of an n-gon from the scratch, we propose the algorithm making the triangulation of an (n+1)-gon on the base of already found triangulations of an n-gon. For such a purpose we must maintain suitable file storage to store previously derived triangulations and later use them to generate the triangulations of polygon with one more vertex. The file storage is partially exploited for elimination of duplicates our algorithm produces. Yet, triangulation and elimination of duplicates do not critically decrease our algorithm performances for smaller values of n

Computing Tensor Generalized bilateral inverses

We introduce tensor generalized bilateral inverses (TGBIs) under the Einstein tensor product as an extension of generalized bilateral inverses (GBIs) in the matrix environment. Moreover, the TBGI class includes so far considered composite generalized inverses (CGIs) for matrices and tensors. Applications of TBGIs for solving multilinear systems are presented. The characterizations and representations of TGBI were studied and verified using a specific algebraic approach. Further, a few characterizations of known CGIs (such as CMP, DMP, MPD, MPCEP, and CEPMP) are derived. The main properties of the TGBIs ware exploited and verified through numerical examples.Comment: 18 page

Application of the partitioning method to specific Toeplitz matrices

We propose an adaptation of the partitioning method for determination of theMoore–Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant reduction in the computational time required to calculate the Moore–Penrose inverse of specific Toeplitz matrices of an arbitrary size. The method is implemented in MATLAB, and illustrative examples are presented

Representations and geometrical properties of generalized inverses over fields

In this paper, as a generalization of Urquhart’s formulas, we present a full description of the sets of inner inverses and (B, C)-inverses over an arbitrary field. In addition, identifying the matrix vector space with an affine space, we analyze geometrical properties of the main generalized inverse sets. We prove that the set of inner inverses, and the set of (B, C)-inverses, form affine subspaces and we study their dimensions. Furthermore, under some hypotheses, we prove that the set of outer inverses is not an affine subspace but it is an affine algebraic variety. We also provide lower and upper bounds for the dimension of the outer inverse set.Agencia Estatal de InvestigaciónUniversidad de Alcal

Representations and symbolic computation of generalized inverses over fields

This paper investigates representations of outer matrix inverses with prescribed range and/or none space in terms of inner inverses. Further, required inner inverses are computed as solutions of appropriate linear matrix equations (LME). In this way, algorithms for computing outer inverses are derived using solutions of appropriately defined LME. Using symbolic solutions to these matrix equations it is possible to derive corresponding algorithms in appropriate computer algebra systems. In addition, we give sufficient conditions to ensure the proper specialization of the presented representations. As a consequence, we derive algorithms to deal with outer inverses with prescribed range and/or none space and with meromorphic functional entries.Agencia Estatal de investigaciónUniversidad de Alcal

Recent Theories and Applications in Approximation Theory

Soleymani, F.; Stanimirovic, PS.; Torregrosa Sánchez, JR.; Nik, HS.; Tohidi, E. (2015). Recent Theories and Applications in Approximation Theory. Scientific World Journal. (598279). doi:10.1155/2015/598279S59827

A Novel Iterative Method for Polar Decomposition and Matrix Sign Function

We define and investigate a globally convergent iterative method possessing sixth order of convergence which is intended to calculate the polar decomposition and the matrix sign function. Some analysis of stability and computational complexity are brought forward. The behaviors of the proposed algorithms are illustrated by numerical experiments