35 citations · 54 across the 11 of their papers we have counts for
12 papers
Deriving Algorithms for Triangular Tridiagonalization a Skew-Symmetric Matrix
Robert van de Geijn, Maggie Myers, RuQing G. Xu +1
This paper provides technical details regarding the application of the FLAME methodology to derive algorithms hand in hand with their proofs of correctness for the computation of t…
Enabling Pivoting in the Formal Derivation of LU factorization
Robert van de Geijn, Margaret E. Myers, Devangi N. Parikh +2
The FLAME methodology for deriving linear algebra algorithms from specification, first introduced around 2000, has been successfully applied to a broad cross section of operations.…
Cascading GEMM: High Precision from Low Precision
Devangi N. Parikh, Robert A. van de Geijn, Greg M. Henry
This paper lays out insights and opportunities for implementing higher-precision matrix-matrix multiplication (GEMM) from (in terms of) lower-precision high-performance GEMM. The d…
GEMMFIP: Unifying GEMM in BLIS
RuQing G. Xu, Field G. Van Zee, Robert A. van de Geijn
Matrix libraries often focus on achieving high performance for problems considered to be either "small" or "large", as these two scenarios tend to respond best to different optimiz…
Strassen's Algorithm for Tensor Contraction
Jianyu Huang, Devin A. Matthews, Robert A. van de Geijn
Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While S…
A Tight I/O Lower Bound for Matrix Multiplication
Tyler Michael Smith, Bradley Lowery, Julien Langou +1
A tight lower bound for required I/O when computing an ordinary matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker low…
A Case for Malleable Thread-Level Linear Algebra Libraries: The LU Factorization with Partial Pivoting
Sandra Catalán, José R. Herrero, Enrique S. Quintana-Ortí +2
We propose two novel techniques for overcoming load-imbalance encountered when implementing so-called look-ahead mechanisms in relevant dense matrix factorizations for the solution…
Generating Families of Practical Fast Matrix Multiplication Algorithms
Jianyu Huang, Leslie Rice, Devin A. Matthews +1
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often…
Automating the Last-Mile for High Performance Dense Linear Algebra
Richard Michael Veras, Tze Meng Low, Tyler Michael Smith +2
High performance dense linear algebra (DLA) libraries often rely on a general matrix multiply (Gemm) kernel that is implemented using assembly or with vector intrinsics. In particu…
BLISlab: A Sandbox for Optimizing GEMM
Jianyu Huang, Robert A. van de Geijn
Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introdu…
Householder QR Factorization with Randomization for Column Pivoting (HQRRP). FLAME Working Note #78
Per-Gunnar Martinsson, Gregorio Quintana-Orti, Nathan Heavner +1
A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matr…
Exploiting Symmetry in Tensors for High Performance: Multiplication with Symmetric Tensors
Martin D. Schatz, Tze Meng Low, Robert A. van de Geijn +1
Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a d…