Related papers: On the Exponentiation of Interval Matrices
Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or time-dependent partial differential equations. For the efficiency of such exponential…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincar\'e inequalities. Typically two kind of sensitivity indices are linked by a Poincar\'e type inequality, which…
A transfer matrix scaling technique is developed for randomly diluted systems, and applied to the site-diluted Ising model on a square lattice in two dimensions. For each allowed disorder configuration between two adjacent columns, the…
For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent)…
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
We present an algorithmic solution to the problem of incremental belief updating in the context of Monte Carlo inference in Bayesian statistical models represented by probabilistic programs. Given a model and a sample-approximated…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast…
Matrix regularity is a key to various problems in applied mathematics. The sufficient conditions, used for checking regularity of interval parametric matrices, usually fail in case of large parameter intervals. We present necessary and…
The extent of parallelization of a loop is largely determined by the dependences between its statements. While dependence free loops are fully parallelizable, those with loop carried dependences are not. Dependence distance is a measure of…
In our work, we consider the linear least squares problem for $m\times n$-systems of linear equations $Ax = b$, $m\geq n$, such that the matrix $A$ and right-hand side vector $b$ can vary within an interval $m\times n$-matrix and an…
We present a novel machine learning architecture that uses the exponential of a single input-dependent matrix as its only nonlinearity. The mathematical simplicity of this architecture allows a detailed analysis of its behaviour, providing…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
Discretization methods for ordinary differential equations based on the use of matrix exponentials have been known for decades. This set of ideas has come off age and acquired greater urgency recently, within the context of geometric…
Solving a system of nonlinear inequalities is an important problem for which conventional numerical analysis has no satisfactory method. With a box-consistency algorithm one can compute a cover for the solution set to arbitrarily close…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with…