Related papers: Faster modular composition using two relation matr…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…
We present a new algorithm for fast matrix multiplication using tensor decompositions which have special features. Thanks to these features we obtain exponents lower than what the rank of the tensor decomposition suggests. In particular for…
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case…
This paper introduces a deterministic algorithm for solving an instance of the Subset Sum Problem based on a new method entitled the Bipartite Synthesis Method. The algorithm is described and shown to have worst-case limiting performance…
We develop the first fast spectral algorithm to decompose a random third-order tensor over $\mathbb{R}^d$ of rank up to $O(d^{3/2}/\text{polylog}(d))$. Our algorithm only involves simple linear algebra operations and can recover all…
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…
We study algorithms for the fast computation of modular inverses. Newton-Raphson iteration over $p$-adic numbers gives a recurrence relation computing modular inverse modulo $p^m$, that is logarithmic in $m$. We solve the recurrence to…
Many applications, including rank aggregation and crowd-labeling, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns. We consider the problem of estimating such a matrix based on…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…
Learning compact and interpretable representations is a very natural task, which has not been solved satisfactorily even for simple binary datasets. In this paper, we review various ways of composing experts for binary data and argue that…
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…
Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of…
Recently increasing penetration of renewable energy generation brings challenges for power system operators to perform efficient power generation daily scheduling, due to the intermittent nature of the renewable generation and discrete…
Solving quadratic equations over finite fields is a fundamental task in algebraic coding theory and serves as a key subroutine for computing the roots of cubic and quartic polynomials. Notably, any quadratic polynomial over binary extension…
We show new algorithms and constructions over linear delta-matroids. We observe an alternative representation for linear delta-matroids, as a contraction representation over a skew-symmetric matrix. This is equivalent to the more standard…
We consider a monotone submodular maximization problem whose constraint is described by a logic formula on a graph. Formally, we prove the following three `algorithmic metatheorems.' (1) If the constraint is specified by a monadic…
Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature,…