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Many numerical problems with input $x$ and output $y$ can be formulated as a system of equations $F(x, y) = 0$ where the goal is to solve for $y$. The condition number measures the change of $y$ for small perturbations to $x$. From this…
This article considers the problem of solving a system of $n$ real polynomial equations in $n+1$ variables. We propose an algorithm based on Newton's method and subdivision for this problem. Our algorithm is intended only for nondegenerate…
An apriori bound for the condition number associated to each of the following problems is given: general linear equation solving, minimum squares, non-symmetric eigenvalue problems, solving univariate polynomials, solving systems of…
Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to study the case of a multiobjective optimization problem…
The tensor rank decomposition problem consists of recovering the unique set of parameters representing a robustly identifiable low-rank tensor when the coordinate representation of the tensor is presented as input. A condition number for…
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…
The validity OF a causal model can be tested ONLY IF the model imposes constraints ON the probability distribution that governs the generated data. IN the presence OF unmeasured variables, causal models may impose two types OF constraints :…
We characterise the sensitivity of several additive tensor decompositions with respect to perturbations of the original tensor. These decompositions include canonical polyadic decompositions, block term decompositions, and sums of tree…
In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition…
Many NP-complete problems take integers as part of their input instances. These input integers are generally binarized, that is, provided in the form of the "binary" numeral representation, and the lengths of such binary forms are used as a…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
A nonlinear algebraic equation system of two variables is numerically solved, which is derived from a nonlinear algebraic equation system of four variables, that corresponds to a mathematical model related to investment under conditions of…
When evaluating causal influence from one time series to another in a multivariate dataset it is necessary to take into account the conditioning effect of the other variables. In the presence of many variables, and possibly of a reduced…
Factors are categorical variables, and the values which these variables assume are called levels. In this paper, we consider the variable selection problem where the set of potential predictors contains both factors and numerical variables.…
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and…
In this paper we investigate the behavior of the condition number of the stiffness matrix resulting from the approximation of a 2D Poisson problem by means of the Virtual Element Method. It turns out that ill-conditioning appears when…
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…
Conditioning on some set of confounders that causally affect both treatment and outcome variables can be sufficient for eliminating bias introduced by all such confounders when estimating causal effect of the treatment on the outcome from…
In solving a system of $n$ linear equations in $d$ variables $Ax=b$, the condition number of the $n,d$ matrix $A$ measures how much errors in the data $b$ affect the solution $x$. Estimates of this type are important in many inverse…
We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…