Related papers: A Generalized Recursive Algorithm for Binary Multi…
In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…
Program synthesis with Genetic Programming searches for a correct program that satisfies the input specification, which is usually provided as input-output examples. One particular challenge is how to effectively handle loops and recursion…
Directional estimation is a common problem in many tracking applications. Traditional filters such as the Kalman filter perform poorly because they fail to take the periodic nature of the problem into account. We present a recursive filter…
We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic…
We consider three different ways of algorithmization of the Janashia-Lagvilava spectral factorization method. The first algorithm is faster than the second one, however, it is only suitable for matrices of low dimension. The second…
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field.We use geometric considerations on the space…
We propose theoretical and empirical improvements for two-stage hashing methods. We first provide a theoretical analysis on the quality of the binary codes and show that, under mild assumptions, a residual learning scheme can construct…
We demonstrate a multiplication method based on numbers represented as set of polynomial radix 2 indices stored as an integer list. The 'polynomial integer index multiplication' method is a set of algorithms implemented in python code. We…
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…
This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the…
The simplex algorithm has been successfully used for many years in solving linear programming (LP) problems. Due to the intensive computations required (especially for the solution of large LP problems), parallel approaches have also…
Matrix-matrix multiplication is a key computational kernel for numerous applications in science and engineering, with ample parallelism and data locality that lends itself well to high-performance implementations. Many matrix…
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm efficiently. The…
The alternating direction method of multipliers (ADMM) is a powerful operator splitting technique for solving structured convex optimization problems. Due to its relatively low per-iteration computational cost and ability to exploit…
Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep…
Sorting is a common and ubiquitous activity for computers. It is not surprising that there exist a plethora of sorting algorithms. For all the sorting algorithms, it is an accepted performance limit that sorting algorithms are linearithmic…
We present a non-commutative algorithm for the multiplication of a 2 x 2 block-matrix by its adjoint, defined by a matrix ring anti-homomorphism. This algorithm uses 5 block products (3 recursive calls and 2 general products)over C or in…
The Kernel Polynomial Method (KPM) is one of the fast diagonalization methods used for simulations of quantum systems in research fields of condensed matter physics and chemistry. The algorithm has a difficulty to be parallelized on a…