Related papers: Minimum Variance Solution of Underdetermined Syste…
We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image…
In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…
Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The…
We define the min-min expectation selection problem (resp. max-min expectation selection problem) to be that of selecting k out of n given discrete probability distributions, to minimize (resp. maximize) the expectation of the minimum value…
In this paper we investigate a problem of state estimation for the dynamical system described by the linear operator equation with unknown parameters in Hilbert space. We present explicit expressions for linear minimax estimation and error…
We introduce a new class of "random" subsets of natural numbers, WM sets. This class contains normal sets (sets whose characteristic function is a normal binary sequence). We establish necessary and sufficient conditions for solvability of…
The condition number of solutions to full rank linear least-squares problem are shown to be given by an optimization problem that involves nuclear norms of rank 2 matrices. The condition number is with respect to the least-squares…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
The problem is considered of arranging symbols around a cycle, in such a way that distances between different instances of a same symbol be as uniformly distributed as possible. A sequence of moments is defined for cycles, similarly to the…
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
Given a linear unknown system with $m$ inputs, $p$ outputs, $n$ dimensional state vector, and $q$ dimensional ecosystem, the problem of the adaptive optimal output regulation of this system boils down to iteratively solving a set of linear…
Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on $\mathbb{E} = [0, \infty]^d \backslash \{(0,0, ..., 0) \} $ and models another regular variation on the sub-cone $\mathbb{E}^{(2)} =…
Newton method is one of the most powerful methods for finding solutions of nonlinear equations and for proving their existence. In its "pure" form it has fast convergence near the solution, but small convergence domain. On the other hand…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
The celebrated minimum residual method (MINRES), proposed in the seminal paper of Paige and Saunders, has seen great success and widespread use in solving Hermitian (and complex-symmetric) linear systems. Unless the system is consistent,…
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…
Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied…
A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…
A novel approach for solving linear estimation problem in multi-user massive MIMO systems is proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the dot product. The general…