相关论文: An Experimental Comparison of Methods for Computin…
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
The $1/x^{2}$ deformed $c=1$ matrix model is studied at finite radius and non-zero cosmological constant. Calculational techniques are presented and illustrated in some examples. Furthermore, a new kind of $R \rightarrow 1/R$ duality is…
Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant…
We improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set $K\subset \mathbb{R}^n$ contained in a box of radius $R$, we show how to either find a…
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
In this paper, the optimality of ternary arithmetic is investigated under strict mathematical formulation. The arithmetic systems are presented in generic form, as the means to encode numeric values, and the choice of radix is asserted as…
The most common method for calculating accurate numerical solutions for complicated linear differential equations - for example, finding eigenvalues and eigenfunctions of the Schrodinger equation for many-electron atoms - is the variational…
Until this work, the packing radius of a poset code was only known in the cases where the poset was a chain, a hierarchy, a union of disjoint chains of the same size, and for some families of codes. Our objective is to approach the general…
Comparative evaluation lies at the heart of science, and determining the accuracy of a computational method is crucial for evaluating its potential as well as for guiding future efforts. However, metrics that are typically used have…
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…
The study of solving the inverse eigenvalue problem for nonnegative matrices has been around for decades. It is clear that an inverse eigenvalue problem is trivial if the desirable matrix is not restricted to a certain structure. Provided…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
It is folklore particularly in numerical and computer sciences that, instead of solving some general problem f:A->B, additional structural information about the input x in A (that is any kind of promise that x belongs to a certain subset A'…