相关论文: Computational Serendipity and Tensor Product Finit…
The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
In this paper, we discuss how to efficiently evaluate and assemble general finite element variational forms on H(div) and H(curl). The proposed strategy relies on a decomposition of the element tensor into a precomputable reference tensor…
Let $J_r$ denote an $r\times r$ matrix over a finite field $F$ with minimal and characteristic polynomials $(t-1)^r$. Suppose $r\leq s$. It is not hard to show that the Jordan canonical form of $J_r\otimes J_s$ is similar to…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
Matrices are built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums or multiplication of matrices are such procedures and a matrix built from these is said to be a {\em separable} matrix. A…
We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices…
In this paper, the first family of conforming finite element divdiv complexes on cuboid grids in three dimensions is constructed. Besides, a new family of conforming finite element divdiv complexes with enhanced smoothness on tetrahedral…
A new family of mixed finite elements is proposed for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. For two dimensions, the normal stress of the matrix-valued stress field is approximated by an enriched…
Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…
In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric H(div)-Pk…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope and tetrahedral prism elements. More generally, our objective is to construct finite…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
QCD sum rules for the determination of form factors of $\Lambda_b$ and $\Lambda_c$ semileptonic decays are investigated. With a form for the baryonic current appropriate for the limits of the heavy quark symmetries, the different tensor…
We present a new set of basis functions for H(curl)-conforming, H(div)-conforming, and L2 -conforming finite elements of arbitrary order on a tetrahedron. The basis functions are expressed in terms of Bernstein polynomials and augment the…
The stability, robustness, accuracy, and efficiency of space-time finite element methods crucially depend on the choice of approximation spaces for test and trial functions. This is especially true for high-order, mixed finite element…
Several notions of code products are known in quantum error correction, such as hyper-graph products, homological products, lifted products, balanced products, to name a few. In this paper we introduce a new product code construction which…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
An efficient coordinate-free notation is elucidated for differentiating matrix expressions and other functions between higher-dimensional vector spaces. This method of differentiation is known, but not explained well, in the literature.…