arXiv subjects

A. A. Karawia

Publications and source records attributed to A. A. Karawia.

9 recordsLinked to original sources

arXiv2015

On Solving Pentadiagonal Linear Systems via Transformations

Many authors studied numeric algorithms for solving the linear systems of the pentadiagonal type. The well-known Fast Pentadiagonal System Solver algorithm is an example of such algorithms. The current article are described new numeric and symbolic algorithms for solving pentadiagonal linear systems via transformations. New algorithms are natural generalization of the work presented in [Moawwad El- Mikkawy and Faiz Atlan, Algorithms for Solving Linear Systems of Equations of Tridiagonal Type via Transformations, Applied Mathematics, 2014, 5, 413-422]. The symbolic algorithms remove the cases where the numeric algorithms fail. The computational cost of our algorithms is given. Some examples are given in order to illustrate the effectiveness of the proposed algorithms. All of the experiments are performed on a computer with the aid of programs written in MATLAB.

math.NA↗

arXiv2014

On the Inverting of A General Heptadiagonal Matrix

In this paper, we developed new numeric and symbolic algorithms to find the inverse of any nonsingular heptadiagonal matrix. Symbolic algorithm will not break and it is without setting any restrictive conditions. The computational cost of our algorithms is $O(n)$. The algorithms are suitable for implementation using computer algebra system such as MAPLE, MATLAB and MATHEMATICA. Examples are given to illustrate the efficiency of the algorithms.

math.NA↗

arXiv2013

New Symbolic Algorithms For Solving A General Bordered Tridiagonal Linear System

In this paper, the author present reliable symbolic algorithms for solving a general bordered tridiagonal linear system. The first algorithm is based on the LU decomposition of the coefficient matrix and the computational cost of it is O(n). The second is based on The Sherman-Morrison-Woodbury formula. The algorithms are implementable to the Computer Algebra System (CAS) such as MAPLE, MATLAB and MATHEMATICA. Three examples are presented for the sake of illustration.

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arXiv2012

A New Recursive Algorithm For Inverting A General Comrade Matrix

In this paper, the author present a reliable symbolic computational algorithm for inverting a general comrade matrix by using parallel computing along with recursion. The computational cost of our algorithm is O(n^2). The algorithm is implementable to the Computer Algebra System (CAS) such as MAPLE, MATLAB and MATHEMATICA. Three examples are presented for the sake of illustration.

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arXiv2010

A New Algorithm for General Cyclic Heptadiagonal Linear Systems Using Sherman-Morrison-Woodbury formula

In this paper, a new efficient computational algorithm is presented for solving cyclic heptadiagonal linear systems based on using of heptadiagonal linear solver and Sherman-Morrison-Woodbury formula. The implementation of the algorithm using computer algebra systems (CAS) such as MAPLE and MATLAB is straightforward. Numerical example is presented for the sake of illustration.

math.NA↗

arXiv2010

A New Algorithm for Inverting General Cyclic Heptadiagonal Matrices Recursively

In this paper, we describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The algorithm is implementable to the Computer Algebra System(CAS) such as MAPLE, Matlab and Mathematica . An example is presented for the sake of illustration.

cs.SC↗

arXiv2010

On the Inverse Of General Cyclic Heptadiagonal and Anti-Heptadiagonal Matrices

In the current work, the author present a symbolic algorithm for finding the determinant of any general nonsingular cyclic heptadiagonal matrices and inverse of anti-cyclic heptadiagonal matrices. The algorithms are mainly based on the work presented in [A. A. KARAWIA, A New Algorithm for Inverting General Cyclic Heptadiagonal Matrices Recursively, arXiv:1011.2306v1 [cs.SC]]. The symbolic algorithms are suited for implementation using Computer Algebra Systems (CAS) such as MATLAB, MAPLE and MATHEMATICA. An illustrative example is given.

cs.SC↗

arXiv2009

Nearly Pentadiagonal Linear Systems

In this paper we present efficient computational and symbolic algorithms for solving a nearly pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS)such as MAPLE, MACSYMA, MATHEMATICA, and MATLAB is straightforward. Two examples are given in order to illustrate the algorithms.

math.NA↗

arXiv2008

Two Algorithms for Solving A General Backward Pentadiagonal Linear Systems

In this paper we present an efficient computational and symbolic algorithms for solving a backward pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS) such as MAPLE, MACSYMA, MATHEMATICA, and MATLAB are straightforward. An examples are given in order to illustrate the algorithms. The symbolic algorithm is competitive the other methods for solving a backward pentadiagonal linear systems.

cs.SC↗