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A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion…
Using the slow triangle map (a type of multi-dimensional continued fraction algorithm), we exhibit a method for generating any number of new identities for subsets of integer partitions.
Compression of inverted lists with methods that support fast intersection operations is an active research topic. Most compression schemes rely on encoding differences between consecutive positions with techniques that favor small numbers.…
We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…
In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval…
In this work a rationalized algorithm for calculating the quotient of two complex numbers is presented which reduces the number of underlying real multiplications. The performing of a complex number division using the naive method takes 4…
A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations…
This paper presents an integer decomposition method. The method first writes an integer as a polynomial with 2 as variable that its coefficients are zero or one. Then, suppose that an integer is decomposed into product of such two…
In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This is a fundamental problem in query complexity, and appears in many contexts, particularly…
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…
A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then we use polyadic techniques…
A universal generator for integer-valued square-integrable random variables is introduced. The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables. The proposal…
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…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
The problem of representing a given positive integer as a sum of four squares of integers has been widely concerned for a long time, and for a given positive odd $n$ one can find a representation by doing arithmetic in a maximal order of…
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and…
Finding desired information from large data set is a difficult problem. Information retrieval is concerned with the structure, analysis, organization, storage, searching, and retrieval of information. Index is the main constituent of an IR…