Related papers: An Abstraction-Preserving Block Matrix Implementat…
Multi-robot path planning is difficult due to the combinatorial explosion of the search space with every new robot added. Complete search of the combined state-space soon becomes intractable. In this paper we present a novel form of…
Distributed-memory matrix multiplication (MM) is a key element of algorithms in many domains (machine learning, quantum physics). Conventional algorithms for dense MM rely on regular/uniform data decomposition to ensure load balance. These…
The partial transpose of a block matrix M is the matrix obtained by transposing the blocks of M independently. We approach the notion of partial transpose from a combinatorial point of view. In this perspective, we solve some basic…
Many matrices associated with fast transforms posess a certain low-rank property characterized by the existence of several block partitionings of the matrix, where each block is of low rank. Provided that these partitionings are known,…
One of the factors that limits the scale, performance, and sophistication of distributed applications is the difficulty of concurrently executing them on multiple distributed computing resources. In part, this is due to a poor understanding…
Hierarchical matrices are space and time efficient representations of dense matrices that exploit the low rank structure of matrix blocks at different levels of granularity. The hierarchically low rank block partitioning produces…
Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of this property is fairly simple for particle methods, e.g.,…
We introduce a data distribution scheme for $\mathcal{H}$-matrices and a distributed-memory algorithm for $\mathcal{H}$-matrix-vector multiplication. Our data distribution scheme avoids an expensive $\Omega(P^2)$ scheduling procedure used…
We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
The eigenvectors of the particle number operator in second quantization are characterized by the block sparsity of their matrix product state representations. This is shown to generalize to other classes of operators. Imposing block…
The new generation of machine learning processors have evolved from multi-core and parallel architectures that were designed to efficiently implement matrix-vector-multiplications (MVMs). This is because at the fundamental level, neural…
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly…
A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented. The key idea is to establish a relationship between a matrix and its full…
Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative…
The ability to express a program as a hierarchical composition of parts is an essential tool in managing the complexity of software and a key abstraction this provides is to separate the representation of data from the computation. Many…
This is the second of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The first paper presented the original algorithm, its…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…