Related papers: The Gauss quadrature for general linear functional…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…
In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include $O_\epsilon(m)$-time algorithms for $(1-\epsilon)$-maximum weight $f$-factor and…
The problem of polynomial least squares fitting in the standard Lagrange basis is addressed in this work. Although the matrices involved in the corresponding overdetermined linear systems are not totally positive, rectangular totally…
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
We develope the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke $L$-functions in the Gaussian field using multiple Dirichlet series under the generalized…
Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
We describe a Lanczos-based algorithm for approximating the product of a rational matrix function with a vector. This algorithm, which we call the Lanczos method for optimal rational matrix function approximation (Lanczos-OR), returns the…
Multiple orthogonality is considered in the realm of a Gauss--Borel factorization problem for a semi-infinite moment matrix. Perfect combinations of weights and a finite Borel measure are constructed in terms of M-Nikishin systems. These…
We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have…
Stieltjes, Perron, and Markov in analysis of the moment problem, for absolutely continuous measures, constructed the underlying measure as the discontinuity across the cut of a Cauchy representation of an otherwise real-analytic function.…
The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator concavity property leads to numerous concavity and convexity results for other matrix…
Classical results show that gradient descent converges linearly to minimizers of smooth strongly convex functions. A natural question is whether there exists a locally nearly linearly convergent method for nonsmooth functions with quadratic…
This paper is about the general truncated matrix-valued moment problem. Let $\mathcal{H}_q$ denote the complex Hermitian $q\times q$-matrices, $q\in \mathbb{N}$. Suppose that $(\mathcal{X},\mathfrak{X})$ is a measurable space and…
Algorithms for computing the classical Gaussian quadrature rules (Gauss--Jacobi, Gauss--Laguerre, and Gauss--Hermite) are presented, based on globally convergent fourth-order iterative methods combined with asymptotic approximations, which…
Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…
We present the FuSSO, a functional analogue to the LASSO, that efficiently finds a sparse set of functional input covariates to regress a real-valued response against. The FuSSO does so in a semi-parametric fashion, making no parametric…
This paper presents a novel systematic methodology to obtain new simple and tight approximations, lower bounds, and upper bounds for the Gaussian Q-function, and functions thereof, in the form of a weighted sum of exponential functions.…