Related papers: A Hybrid Numerical Algorithm for Evaluating n-th O…
Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
Primal-Dual Hybrid Gradient (PDHG) and Alternating Direction Method of Multipliers (ADMM) are two widely-used first-order optimization methods. They reduce a difficult problem to simple subproblems, so they are easy to implement and have…
The primal-dual hybrid gradient method (PDHG) is useful for optimization problems that commonly appear in image reconstruction. A downside of PDHG is that there are typically three user-set parameters and performance of the algorithm is…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…
The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at…
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During the course of the algorithm partial…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
We consider the problem of triangulating a polygon with $n$ vertices and $h$ holes, or relatedly the problem of computing the trapezoidal decomposition of a collection of $h$ disjoint simple polygonal chains with $n$ vertices total.…
We consider the following problem: given three sets of real numbers, output a word-RAM data structure from which we can efficiently recover the sign of the sum of any triple of numbers, one in each set. This is similar to a previous work by…
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
An algorithm for image processing is proposed. The proposed algorithm, which can be viewed as a quantum-classical hybrid algorithm, can transform a low-resolution bitonal image of a character from the set of alphanumeric characters (A-Z,…
In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…
We compute the $n_h$ terms to the massive three loop vector-, axialvector-, scalar- and pseudoscalar form factors in a direct analytic calculation using the method of large moments. This method has the advantage, that the master integrals…
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…
We study on-line strategies for solving problems with hybrid algorithms. There is a problem Q and w basic algorithms for solving Q. For some lambda <= w, we have a computer with lambda disjoint memory areas, each of which can be used to run…
I present a numerical algorithm for direct evaluation of multiple Grassmann integrals. The approach is exact and suffers no Fermion sign problems. Memory requirements grow exponentially with the interaction range and the transverse size of…
We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…