The paper establishes explicit representations of the errors and residuals of approximate
solutions of triangular linear systems by Jordan elimination and of general linear algebraic
systems by Gauss-Jordan elimination as functions of the data perturbations and the rounding
errors in arithmetic floating-point operations. From these representations strict optimal
componentwise error and residual bounds are derived. Further, stability estimates for the
solutions are discussed. The error bounds for the solutions of triangular linear systems are
compared to the optimal error bounds for the solutions by back substitution and by Gaussian
elimination with back substitution, respectively. The results confirm in a very detailed form
that the errors of the solutions by Jordan elimination and by Gauss-Jordan elimination cannot
be essentially greater than the possible maximal errors of the solutions by back substitution
and by Gaussian elimination, respectively. Finally, the theoretical results are illustrated by
two numerical examples.
Perhaps going to watch movies in cinemas today has become different from what it was before. The cinematic film, the clarity of the image and the luster of its colors pulled the rug out from under the most important change that occurred in the structure of the contemporary cinematography, which is the sound. The surround sound environment that immerses viewers in the realism of sound that reaches them from all directions, and for this the researcher found it necessary to shed light on this topic because of its importance, so the research problem was represented in the following question: (How are modern sound systems used in the structure of contemporary feature films?) The theoretical framework included two topics: the first: the dialec
... Show More<p>The popularity, great influence and huge importance made wireless indoor localization has a unique touch, as well its wide successful on positioning and tracking systems for both human and assists also contributing to take the lead from outdoor systems in the scope of the recent research works. In this work, we will attempt to provide a survey of the existing indoor positioning solutions and attempt to classify different its techniques and systems. Five typical location predication approaches (triangulation, fingerprinting, proximity, vision analysis and trilateration) are considered here in order to analysis and provide the reader a review of the recent advances in wireless indoor localization techniques and systems to hav
... Show MoreA range of macrocyclic dinuclear metal (II) dithiocarbamate-based complexes are reported. The preparation of complexes was accomplished from either mixing of the prepared ligand with a metal ion or through a template one-pot reaction. The preparation of the bisamine precursor was achieved through several synthetic steps. The free ligand; potassium 2,2'-(biphenyl-4,4'-diylbis(azanediyl))bis(1-chloro-2-oxoethane-2,1diyl)bis(cyclohexylcarbamodithioate) (L) was yielded from the addition of CS2 to a bis-amine precursor in KOH medium.A variety of analytical and physical methods were implemented to characterise ligand and its complexes. The analyses were based on spectroscopic techniques (FTIR, UV-Vis, mass spectroscopy and 1H, 13C-NMR sp
... Show MoreLongitudinal data is becoming increasingly common, especially in the medical and economic fields, and various methods have been analyzed and developed to analyze this type of data.
In this research, the focus was on compiling and analyzing this data, as cluster analysis plays an important role in identifying and grouping co-expressed subfiles over time and employing them on the nonparametric smoothing cubic B-spline model, which is characterized by providing continuous first and second derivatives, resulting in a smoother curve with fewer abrupt changes in slope. It is also more flexible and can pick up on more complex patterns and fluctuations in the data.
The longitudinal balanced data profile was compiled into subgroup
... Show MoreNecessary and sufficient conditions for the operator equation I AXAX n  ï€* , to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.
The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex
... Show MoreThis paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.
The linear segment with parabolic blend (LSPB) trajectory deviates from the specified waypoints. It is restricted to that the acceleration must be sufficiently high. In this work, it is proposed to engage modified LSPB trajectory with particle swarm optimization (PSO) so as to create through points on the trajectory. The assumption of normal LSPB method that parabolic part is centered in time around waypoints is replaced by proposed coefficients for calculating the time duration of the linear part. These coefficients are functions of velocities between through points. The velocities are obtained by PSO so as to force the LSPB trajectory passing exactly through the specified path points. Also, relations for velocity correction and exact v
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