The current paper is mainly devoted to construct a generalized symbolic Thomas algorithm that will never fail. Two new efficient and reliable computational algorithms are given. The algorithms are suited for implement...The current paper is mainly devoted to construct a generalized symbolic Thomas algorithm that will never fail. Two new efficient and reliable computational algorithms are given. The algorithms are suited for implementation using computer algebra systems (CAS) such as Mathematica, Macsyma and Maple. Some illustrative examples are given.展开更多
The current paper is mainly devoted for solving centrosymmetric linear systems of equations. Formulae for the determinants of tridiagonal centrosymmetric matrices are obtained explicitly. Two efficient computational a...The current paper is mainly devoted for solving centrosymmetric linear systems of equations. Formulae for the determinants of tridiagonal centrosymmetric matrices are obtained explicitly. Two efficient computational algorithms are established for solving general centrosymmetric linear systems. Based on these algorithms, a MAPLE procedure is written. Some illustrative examples are given.展开更多
This paper presents new numeric and symbolic algorithms for solving doubly bordered tridiagonal linear system. The proposed algorithms are derived using partition together with UL factorization. Inversion algorithm fo...This paper presents new numeric and symbolic algorithms for solving doubly bordered tridiagonal linear system. The proposed algorithms are derived using partition together with UL factorization. Inversion algorithm for doubly bordered tridiagonal matrix is also considered based on the Sherman-Morrison-Woodbury formula. The algorithms are implemented using the computer algebra system, MAPLE. Some illustrative examples are given.展开更多
Numeric algorithms for solving the linear systems of tridiagonal type have already existed. The well-known Thomas algorithm is an example of such algorithms. The current paper is mainly devoted to constructing symboli...Numeric algorithms for solving the linear systems of tridiagonal type have already existed. The well-known Thomas algorithm is an example of such algorithms. The current paper is mainly devoted to constructing symbolic algorithms for solving tridiagonal linear systems of equations via transformations. The new symbolic algorithms remove the cases where the numeric algorithms fail. The computational cost of these algorithms is given. MAPLE procedures based on these algorithms are presented. Some illustrative examples are given.展开更多
In the current paper, the authors present a symbolic algorithm for solving doubly bordered k-tridiagonal linear system having n equations and n unknowns. The proposed algorithm is derived by using partition together w...In the current paper, the authors present a symbolic algorithm for solving doubly bordered k-tridiagonal linear system having n equations and n unknowns. The proposed algorithm is derived by using partition together with UL factorization. The cost of the algorithm is O(n). The algorithm is implemented using the computer algebra system, MAPLE. Some illustrative examples are given.展开更多
The present article is mainly devoted for solving bordered k-tridiagonal linear systems of equations. Two efficient and reliable symbolic algorithms for solving such systems are constructed. The computational cost of ...The present article is mainly devoted for solving bordered k-tridiagonal linear systems of equations. Two efficient and reliable symbolic algorithms for solving such systems are constructed. The computational cost of the algorithms is obtained. Some illustrative examples are given.展开更多
In the current article we propose a new efficient, reliable and breakdown-free algorithm for solving general opposite-bordered tridiagonal linear systems. An explicit formula for computing the determinant of an opposi...In the current article we propose a new efficient, reliable and breakdown-free algorithm for solving general opposite-bordered tridiagonal linear systems. An explicit formula for computing the determinant of an opposite-bordered tridiagonal matrix is investigated. Some illustrative examples are given.展开更多
文摘The current paper is mainly devoted to construct a generalized symbolic Thomas algorithm that will never fail. Two new efficient and reliable computational algorithms are given. The algorithms are suited for implementation using computer algebra systems (CAS) such as Mathematica, Macsyma and Maple. Some illustrative examples are given.
文摘The current paper is mainly devoted for solving centrosymmetric linear systems of equations. Formulae for the determinants of tridiagonal centrosymmetric matrices are obtained explicitly. Two efficient computational algorithms are established for solving general centrosymmetric linear systems. Based on these algorithms, a MAPLE procedure is written. Some illustrative examples are given.
文摘This paper presents new numeric and symbolic algorithms for solving doubly bordered tridiagonal linear system. The proposed algorithms are derived using partition together with UL factorization. Inversion algorithm for doubly bordered tridiagonal matrix is also considered based on the Sherman-Morrison-Woodbury formula. The algorithms are implemented using the computer algebra system, MAPLE. Some illustrative examples are given.
文摘Numeric algorithms for solving the linear systems of tridiagonal type have already existed. The well-known Thomas algorithm is an example of such algorithms. The current paper is mainly devoted to constructing symbolic algorithms for solving tridiagonal linear systems of equations via transformations. The new symbolic algorithms remove the cases where the numeric algorithms fail. The computational cost of these algorithms is given. MAPLE procedures based on these algorithms are presented. Some illustrative examples are given.
文摘In the current paper, the authors present a symbolic algorithm for solving doubly bordered k-tridiagonal linear system having n equations and n unknowns. The proposed algorithm is derived by using partition together with UL factorization. The cost of the algorithm is O(n). The algorithm is implemented using the computer algebra system, MAPLE. Some illustrative examples are given.
文摘The present article is mainly devoted for solving bordered k-tridiagonal linear systems of equations. Two efficient and reliable symbolic algorithms for solving such systems are constructed. The computational cost of the algorithms is obtained. Some illustrative examples are given.
文摘In the current article we propose a new efficient, reliable and breakdown-free algorithm for solving general opposite-bordered tridiagonal linear systems. An explicit formula for computing the determinant of an opposite-bordered tridiagonal matrix is investigated. Some illustrative examples are given.
