Related papers: A New Algorithm for Inverting General Cyclic Hepta…
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…
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…
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…
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 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.
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…
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…
$k$-diagonal circulant matrices and cyclic banded matrices are widely used in numerical simulations and signal processing of circular linear systems. Algorithms that directly involve or specify linear or quadratic complexity for the…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
In this study, an algorithm for computing the inverse of periodic k banded matrices, which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison,…
This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient…
The computation of generalized inverses of quaternion matrices is a fundamental problem in quaternion linear algebra, with wide-ranging applications in signal processing, image restoration, and multidimensional data analysis. This paper…
If $A$ is a tridiagonal matrix, then the equations $AX=I$ and $XA=I$ defining the inverse $X$ of $A$ are in fact the second order recurrence relations for the elements in each row and column of $X$. Thus, the recursive algorithms should be…
We present a methodology for parallel acceleration of learning in the presence of matrix orthogonality and unitarity constraints of interest in several branches of machine learning. We show how an apparently sequential elementary rotation…