Related papers: A New Algorithm for General Cyclic Heptadiagonal L…
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…
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,…
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)…
The article presents the theoretical background of the algorithms for solving cyclic block tridiagonal and cyclic block penta-diagonal systems of linear algebraic equations present in ref [1] and [2]. The theory is based on the Woodbury…
We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of…
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…
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…
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…
This paper presents a symbolic algorithm for solving band matrix systems of linear algebraic equations with heptadiagonal coefficient matrices. The algorithm is given in pseudocode. A theorem which gives the condition for the algorithm to…
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…
Hierarchical matrices (usually abbreviated ${\mathcal H}$-matrices) are frequently used to construct preconditioners for systems of linear equations. Since it is possible to compute approximate inverses or $LU$ factorizations in ${\mathcal…
Quantum algorithms for solving linear systems of equations have generated excitement because of the potential speed-ups involved and the importance of solving linear equations in many applications. However, applying these algorithms can be…
We present a simple formula to update the pseudoinverse of a full-rank rectangular matrix that undergoes a low-rank modification, and demonstrate its utility for solving least squares problems. The resulting algorithm can be dramatically…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We use the standard multiple shooting method to solve a linear two point boundary-value problem. To ensure that the solution obtained by combining the partial solutions is continuous and satisfies the boundary conditions, we have to solve a…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
In this paper, we compose a computational algorithm for the determinant and the inverse of the n x n cyclic nonadiagonal matrix. The algorithm is suited for implementation using computer algebra systems (CAS) such as Mathematica and Maple.
A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new…
We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…
The objective of this work is to present a novel approach for the solution of Pentadiagonal Toeplitz systems of equations that is both faster and more effective than existing classical direct methods. The distinctive structure of…