Related papers: A Triangular Decomposition Algorithm for Different…
A simple algorithm to compute all the zeros of a generic polynomial is proposed.
In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…
This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…
We analyze the decomposition problem of multivariate polynomial-exponential functions from truncated series and present new algorithms to compute their decomposition. Using the duality between polynomials and formal power series, we first…
We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…
This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…
We present an algorithm for computing a separating linear form of a system of bivariate polynomials with integer coefficients, that is a linear combination of the variables that takes different values when evaluated at distinct (complex)…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
This paper presents a novel algorithm for constructing a sum-of-squares (SOS) decomposition for positive semi-definite polynomials with rational coefficients. Unlike previous methods that typically yield SOS decompositions with…
There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…
We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, that is, expressing them as sums of powers of independent linear forms. It is based on Harrison's center theory and consists of a…
In this paper the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style are studied when the input polynomial set to decompose has a chordal associated graph. In particular, we prove that the…
In this paper, a numerical method is proposed for canonical polyadic (CP) decomposition of small size tensors. The focus is primarily on decomposition of tensors that correspond to small matrix multiplications. Here, rank of the tensors is…
Our objective is to calculate the derivatives of data corrupted by noise. This is a challenging task as even small amounts of noise can result in significant errors in the computation. This is mainly due to the randomness of the noise,…
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper…
We present a framework to decompose real multivariate polynomials while preserving invariance and positivity. This framework has been recently introduced for tensor decompositions, in particular for quantum many-body systems. Here we…
In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We present a zero decomposition theorem and an algorithm based on Wu's method, which computes a zero decomposition with multiplicity for a given zero-dimensional polynomial system. If the system satisfies some condition, the zero…