Related papers: On The Block Decomposition and Spectral Factors of…
We construct a family of test kernels for use in spectral trace formulas on locally symmetric spaces. The key innovation is the factorization $h_T = g_T \star \widetilde{g}_T$, which simultaneously achieves: (i) automatic positive…
We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate factorizations, that is, factorizations with univariate…
In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on…
Data-driven modeling plays an increasingly important role in different areas of engineering. For most of existing methods, such as genetic programming (GP), the convergence speed might be too slow for large scale problems with a large…
Block-matching and 3D filtering (BM3D) is an image denoising algorithm that works in two similar steps. Both of these steps need to perform grouping by block-matching. We implement the block-matching in an FPGA, leveraging its ability to…
Factorial clustering methods have been developed in recent years thanks to the improving of computational power. These methods perform a linear transformation of data and a clustering on transformed data optimizing a common criterion.…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we…
Block-encoding operators are one of the essential components in quantum algorithms based on Quantum Signal Processing. Their gate complexity largely determines the overall gate complexity of the full algorithm. Using variational methods, we…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
We give new algorithms based on the sum-of-squares method for tensor decomposition. Our results improve the best known running times from quasi-polynomial to polynomial for several problems, including decomposing random overcomplete…
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…
Given an arbitrary monic polynomial $f$ over a field $F$ of characteristic 0, we use companion matrices to construct a polynomial $M_f\in F[X]$ of minimum degree such that for each root $\alpha$ of $f$ in the algebraic closure of $F$,…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
Quantum signal processing combined with quantum eigenvalue transformation has recently emerged as a unifying framework for several quantum algorithms. In its standard form, it consists of two separate routines: block encoding, which encodes…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…