We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen’s triangular tridiagonalization. It factors a dense symmetric matrix A as the product A = PLTL TPT where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. The current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.
Publications
Tags
2D
Accelerators
Algorithms
Architectures
Arrays
Big Data
Bootstrapping
C++
Cache Partitioning
Cancer
Careers
Chisel
Communication
Computer Architecture
CTF
DIABLO
Efficiency
Energy
FPGA
GAP
Gaussian Elimination
Genomics
GPU
Hardware
HLS
Lower Bounds
LU
Matrix Multiplication
Memory
Multicore
Oblivious
Open Space
OS
Parallelism
Parallel Reduction
Performance
PHANTOM
Processors
Python
Research Centers
RISC-V
SEJITS
Tall-Skinny QR
Technical Report
Test generation