A cellular computer to implement the kalman filter algorithm

By Lynn E. Cannon. 1969

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Speech & Audio

Citations in the corpus

GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding (2020, methodology): “For certain scenarios, we also implemented an algorithm similar to Cannon’s algorithm [38], in order to limit the size of tensors on each partition.”
Supporting Very Large Models using Automatic Dataflow Graph Partitioning (2018, background): “ystems for tensor computing. The very first effort starts from developing lowlevel, optimized, parallel matrix/tensor libraries [57–61]. These libraries implement efficient parallel matrix algorithms [23, 62] and tensor operations [63]. However, they have very limited programmability support and add”
Scalable task-based algorithm for multiplication of block-rank-sparse matrices (2015, background): “Keywords distributed memory, matrix multiplication, SUMMA, lowrank decomposition, irregular computation, rank-structured, matrix, H matrix, semiseparable matrix, task parallelism, tensor contraction”
Integrated Model, Batch, and Domain Parallelism in Training Neural Networks (2017, methodology): “5D algorithm, as opposed to a 2D algorithm such as Cannon’s algorithm [2] or SUMMA [21].”
Minimizing Communication in Numerical Linear Algebra (2009, methodology): “In the “memory-scalable” case, where each processor stores the minimal O ( n 2 /P ) words of data, they obtain the lower bound Ω(#arithmetic operations per processor / √ memory per processor) = Ω( n 3 /P √ n 2 /P ) = Ω( n 2 √ P ), which is attained by Cannon’s algorithm [Can69] [Dem96, Lecture 11].”
A massively parallel tensor contraction framework for coupled-cluster computations (2014, methodology): “Our paper focuses on parallel algorithms for the execution of a single tensor contraction, leaving it for future work to integrate this single-contraction parallelization with a second layer of multi-contraction parallelism.”
Overlap Communication with Dependent Computation via Decomposition in Large Deep Learning Models (2022, methodology): “Cannon’s algorithm [13] is a widely used 2D algorithm since its first introduction in 1969.”
The potential of the cell processor for scientific computing (2005, methodology): “A possible alternate approach is to adapt Cannon’s algorithm [3] for parallel machines.”
Straggler Mitigation in Distributed Matrix Multiplication: Fundamental Limits and Optimal Coding (2018, background): “Hence, deploying matrix computation tasks on large-scale distributed systems has received wide interests [1]–[4].”
Communication-optimal Parallel and Sequential QR and LU Factorizations (2008, background): “It is well-known that the communication lower bound for sequential matrix multiplication is attained by “tiling” or “blocking” the matrices into square blocks of dimension √ W/3, and for parallel matrix multiplication by Cannon’s algorithm [8].”
Communication lower bounds for distributed-memory matrix multiplication (2004, methodology): “Cannon originally proposed the algorithm for a parallel computer with P = n 2 processors, connected as a two-dimensional mesh.”
Communication optimal parallel multiplication of sparse random matrices (2013, methodology): “The approach that generalizes Cannon’s algorithm [11] is presented as “2.”
Communication-Optimal Parallel 2.5D Matrix Multiplication and LU Factorization Algorithms (2011, background): “If this is the case, it is known that Cannon’s Algorithm [7] simultaneously balances the load (so F = Θ(n3/p)), minimizes the bandwidth cost (so W = Θ(n2/p1/2)), and minimizes the latency cost (so S = Θ(p1/2)) [15, 5].”
Integrated Model and Data Parallelism in Training Neural Networks (2017, methodology): “5D algorithm, as opposed to a 2D algorithm such as Cannon’s algorithm [2] or SUMMA [20].”
CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations. (2020, methodology): “• for general matrices (any size) we use the Cannon algorithm, where the amount of communicated data by each process scales as O(1/ √ P ) [105, 352];”