Related papers: On efficient block Krylov-solvers for $\mathcal H^…
Krylov methods are a key way of solving large sparse linear systems of equations, but suffer from poor strong scalabilty on distributed memory machines. This is due to high synchronization costs from large numbers of collective…
Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering. The crucial computing kernel for such iterative solutions is the multiplication of a…
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case…
The considerable impact of Convolutional Neural Networks on many Artificial Intelligence tasks has led to the development of various high performance algorithms for the convolution operator present in this type of networks. One of these…
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.,…
Hierarchical low-rank approximation of dense matrices can reduce the complexity of their factorization from O(N^3) to O(N). However, the complex structure of such hierarchical matrices makes them difficult to parallelize. The block size and…
Factorization and multiplication of dense matrices and tensors are critical, yet extremely expensive pieces of the scientific toolbox. Careful use of low rank approximation can drastically reduce the computation and memory requirements of…
The GEneral Matrix Multiplication (GEMM) is one of the essential algorithms in scientific computing. Single-thread GEMM implementations are well-optimised with techniques like blocking and autotuning. However, due to the complexity of…
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the…
Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate…
We derive an augmented Krylov subspace method with subspace recycling for computing a sequence of matrix function applications on a set of vectors. The matrix is either fixed or changes as the sequence progresses. We assume consecutive…
With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted…
In the iterative solution of dense linear systems from boundary integral equations or systems involving kernel matrices, the main challenges are the expensive matrix-vector multiplication and the storage cost which are usually tackled by…
In this work we introduce a memory-efficient method for computing the action of a Hermitian matrix function on a vector. Our method consists of a rational Lanczos algorithm combined with a basis compression procedure based on rational…
HipMCL is a high-performance distributed memory implementation of the popular Markov Cluster Algorithm (MCL) and can cluster large-scale networks within hours using a few thousand CPU-equipped nodes. It relies on sparse matrix computations…
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…
Several researchers have developed a rich toolbox of matrix compression techniques that exploit structure and redundancy in large matrices. Classical methods such as the block low-rank format and the Fast Multipole Method make it possible…
This paper presents an efficient technique for matrix-vector and vector-transpose-matrix multiplication in distributed-memory parallel computing environments, where the matrices are unstructured, sparse, and have a substantially larger…
Sparse linear iterative solvers are essential for many large-scale simulations. Much of the runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a sequence of sparse matrix-vector products. A variety…
In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…