Related papers: A new framework for the computation of Hessians
The row (resp. column) rank profile of a matrix describes the staircase shape of its row (resp. column) echelon form. In an ISSAC'13 paper, we proposed a recursive Gaussian elimination that can compute simultaneously the row and column rank…
Graphs and hypergraphs combine expressive modeling power with algorithmic efficiency for a wide range of applications. Hedgegraphs generalize hypergraphs further by grouping hyperedges under a color/hedge. This allows hedgegraphs to model…
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Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…
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We present a new edge selection heuristic and vertex ordering heuristic that together enable one to compute the Tutte polynomial of much larger sparse graphs than was previously doable. As a specific example, we are able to compute the…
We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our…
Estimation of Gaussian graphical models is important in natural science when modeling the statistical relationships between variables in the form of a graph. The sparsity and clustering structure of the concentration matrix is enforced to…
Trust-region (TR) and adaptive regularization using cubics (ARC) have proven to have some very appealing theoretical properties for non-convex optimization by concurrently computing function value, gradient, and Hessian matrix to obtain the…
Computing resonance and anti-resonance backbone curves in complex nonlinear mechanical systems is of high engineering relevance but remains computationally challenging, especially for large finite-element (FE) models. Existing…
We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. Our method is based on expressing the Fisher metric in terms of the posterior distributions…
This paper presents a novel algorithmic framework for the computational design, simulation, and fabrication of a hexagonal grid-based double-curvature structure with planar hexagonal panels. The journey begins with constructing a robust…
We present a novel black box optimization algorithm called Hessian Estimation Evolution Strategy. The algorithm updates the covariance matrix of its sampling distribution by directly estimating the curvature of the objective function. This…
From implicit differentiation to probabilistic modeling, Jacobian and Hessian matrices have many potential use cases in Machine Learning (ML), but they are viewed as computationally prohibitive. Fortunately, these matrices often exhibit…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and…
In this work, we propose a unified abstraction for graph algorithms: the Extended General Einsums language, or EDGE. The EDGE language expresses graph algorithms in the language of tensor algebra, providing a rigorous, succinct, and…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
Although the isogeometric analysis has shown its great potential in achieving highly accurate numerical solutions of partial differential equations, its efficiency is the main factor making the method more competitive in practical…