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Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard…

The Canonical Polyadic (CP) tensor decomposition is a well-known method for interpretable analysis of high-dimensional data. Recently, the Generalized CP method (GCP) was introduced by Hong and Kolda to allow for flexible choice of the loss…

Many large-scale scientific computations require eigenvalue solvers in a scaling regime where efficiency is limited by data movement. We introduce a parallel algorithm for computing the eigenvalues of a dense symmetric matrix, which…

Current high-performance computer systems used for scientific computing typically combine shared memory computational nodes in a distributed memory environment. Extracting high performance from these complex systems requires tailored…

In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a $d$-dimensional $( d \geq 2 )$ simple lattice model. Sequential computation of the HOTRG requires $O ( \chi^{4 d -…

We extend an existing approach for efficient use of shared mapped memory across Chapel and C++ for graph data stored as 1-D arrays to sparse tensor data stored using a combination of 2-D and 1-D arrays. We describe the specific extensions…

Candecomp / PARAFAC (CP) decomposition, a generalization of the matrix singular value decomposition to higher-dimensional tensors, is a popular tool for analyzing multidimensional sparse data. On tensors with billions of nonzero entries,…

We employ pressure point analysis and roofline modeling to identify performance bottlenecks and determine an upper bound on the performance of the Canonical Polyadic Alternating Poisson Regression Multiplicative Update (CP-APR MU) algorithm…

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…

Approximating a tensor in the tensor train (TT) format has many important applications in scientific computing. Rounding a TT tensor involves further compressing a tensor that is already in the TT format. This paper proposes new randomized…

The CANDECOMP/PARAFAC (CP) decomposition is a leading method for the analysis of multiway data. The standard alternating least squares algorithm for the CP decomposition (CP-ALS) involves a series of highly overdetermined linear least…

Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…

We investigate a parallelization strategy for dense matrix factorization (DMF) algorithms, using OpenMP, that departs from the legacy (or conventional) solution, which simply extracts concurrency from a multithreaded version of BLAS. This…

The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…

As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…

Interprocessor communication often dominates the runtime of large matrix computations. We present a parallel algorithm for computing QR decompositions whose bandwidth cost (communication volume) can be decreased at the cost of increasing…

Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…

Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…