Related papers: Efficient computation of the Zassenhaus formula
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indirectly provides rather effective coding of symbols for very…
An elementary approach for computing the values at negative integers of the Riemann zeta function is presented. The approach is based on a new method for ordering the integers and a new method for summation of divergent series. We show that…
We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational logic networks with linear size…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably…
A new definition for the Riemann zeta function for all positive integer number s > 1 is presented. We discover a most elegant expression and easy method for calculating the Riemann zeta function for small even integer values. Through this…
Iterative algorithms are ubiquitous in the field of data mining. Widely known examples of such algorithms are the least mean square algorithm, backpropagation algorithm of neural networks. Our contribution in this paper is an improvement…
An algorithm is presented for generating successive approximations to trigonometric functions of sums of non-commuting matrices. The resulting expressions involve nested commutators of the respective matrices. The procedure is shown to…
Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is…
A new algorithm to compute the restricted singular value decomposition of dense matrices is presented. Like Zha's method \cite{Zha92}, the new algorithm uses an implicit Kogbetliantz iteration, but with four major innovations. The first…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…
We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods for obtaining numerical values of these…
This paper provides an introduction to the design of augmented data structures that offer an efficient representation of a mathematical sequence and fast sequential summation algorithms, which guarantee both logarithmic running time and…
We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which…
Using Bayes's theorem, we derive a unit-wise recurrence as well as a backward recursion similar to the forward-backward algorithm. The resulting Bayesian recurrent units can be integrated as recurrent neural networks within deep learning…
Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…