Related papers: Sparse implicitization by interpolation: Geometric…
This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
Encoding 3D points is one of the primary steps in learning-based implicit scene representation. Using features that gather information from neighbors with multi-resolution grids has proven to be the best geometric encoder for this task.…
Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
Structured prediction requires searching over a combinatorial number of structures. To tackle it, we introduce SparseMAP: a new method for sparse structured inference, and its natural loss function. SparseMAP automatically selects only a…
In this work, we establish theoretical and practical connections between vertex indexing for sparse graph/network compression and matrix ordering for sparse matrix-vector multiplication and variable elimination. We present a fundamental…
Recently a new adaptive path interpolation method has been developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference problems defined on dense factor graphs. These include random…
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…
Interpolation methodologies have been widely used within the domain of indoor positioning systems. However, existing indoor positioning interpolation algorithms exhibit several inherent limitations, including reliance on complex…
We propose a new inertia-revealing factorization for sparse symmetric matrices. The factorization scheme and the method for extracting the inertia from it were proposed in the 1960s for dense, banded, or tridiagonal matrices, but they have…
Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is…
We propose a sparse interpolation construction and a practical coarsening algorithm for the algebraic multigrid (AMG) method, tailored towards H(curl). Building on the generalized AMG framework, we introduce an interior/exterior splitting…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
Motivated by the recent multilevel sparse kernel-based interpolation (MuSIK) algorithm proposed in [Georgoulis, Levesley and Subhan, SIAM J. Sci. Comput., 35(2), pp. A815-A831, 2013], we introduce the new quasi-multilevel sparse…