Related papers: Black Box Linear Algebra: Extending Wiedemann's An…
The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a…
We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…
This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…
We present a new deep learning paradigm for the generation of sparse approximate inverse (SPAI) preconditioners for matrix systems arising from the mesh-based discretization of elliptic differential operators. Our approach is based upon the…
We consider the classical problems of interpolating a polynomial given a black box for evaluation, and of multiplying two polynomials, in the setting where the bit-lengths of the coefficients may vary widely, so-called unbalanced…
We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. The result covers both matrices over finite fields with independent non-zero entries and…
Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. In a previous article, we gave a necessary and sufficient condition for X to be free of given rank d…
Multi-objective optimization is a crucial matter in computer systems design space exploration because real-world applications often rely on a trade-off between several objectives. Derivatives are usually not available or impractical to…
The paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. As the starting point of our programme, we construct Frobenius maps on black box groups of untwisted Lie type in odd…
Side information provides a pivotal role for message delivery in many communication scenarios to accommodate increasingly large data sets, e.g., caching networks. Although index coding provides a fundamental modeling framework to exploit…
We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves…
We propose a novel Riemannian preconditioning approach for the tensor completion problem with rank constraint. A Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into…
The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing…
In this work, we present a new scalable incomplete LU factorization framework called Javelin to be used as a preconditioner for solving sparse linear systems with iterative methods. Javelin allows for improved parallel factorization on…
Sparse matrices are an integral part of scientific simulations. As hardware evolves new sparse matrix storage formats are proposed aiming to exploit optimizations specific to the new hardware. In the era of heterogeneous computing, users…
Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…