Scalable Universal Matrix Multiplication Algorithm

23 Apr, 2021

The paper describes Parallel Universal Matrix Multiplication Algorithms PUMMA on distributed memory concurrent computers. What is the abbreviation for Scalable Universal Matrix Multiplication Algorithm.

Analysis Of A Class Of Parallel Matrix Multiplication Algorithms

The routines perform efficiently for a wide range of.

Scalable universal matrix multiplication algorithm. Choi Jaeyoung David W. It performs the communication-efficient parallel matrix multiplication and is able to recover from compute node failures using redundancy through coded computation. In this paper we give a straight forward highly efficient scalable implementation of common matrix multiplication operations.

In the paper we give a straightforward highly efficient scalable implementation of common matrix multiplication operations. Nur Dean The Graduate Center Matrix Multiplication 05012017 17 36. The algorithms are much simpler than previously published methods yield better performance and require less work space.

We generalize these 2D and 3D algorithms by introducing a new class of 25D algorithms. For matrix multiplication we can take advantage of any amount of extra memory to store c copies of the data for any c 1 2 p 13 to reduce the bandwidth cost of Cannons algorithm by a factor of c 12 and the latency cost by a factor c 32. It is used by the ScaLAPACK PLAPACK and Elemental libraries.

Scalable universal matrix multiplication algorithm. SUMMA is defined as Scalable Universal Matrix Multiplication Algorithm somewhat frequently. Parallel Algorithms for Matrix Multiplication Foxs Algorithm c Compute C ij AB for each process a 01 b 10 c 00 c 00 a 01b 10 a 01 b 11 c 01 c 01 a 01b 11 a 10 b 00 c 10 c 10 a 10b 00 a 10 b 01 c 11 c 11 a 10b 01 The algorithm is complete after n stages and process P ij contains the nal result for c ij.

In this paper we give a straight forward highly efficient scalable implementation of common matrix multiplication operations. Scalable Universal Matrix Multiplication Algorithm - How is Scalable Universal Matrix Multiplication Algorithm abbreviated. The Scalable Universal Matrix Multiplication Algorithm 27 is another algorithm that overcomes all shortcomings of Cannons algorithm and Foxs algorithm.

Parallel universal matrix multiplication algorithms on distributed memory concurrent computers. In this paper we give a straight forward highly e cient scalable implementation of common matrix multiplication operations. The algorithm depends on the following simple formula from linear algebra.

MPI implementations are given as are performance results on the. MPI implementations are given as are performance results on the Intel Paragon system. Van De Geijn Robert A and Jerrell Watts.

SUMMA stands for Scalable Universal Matrix Multiplication Algorithm. We believe it is a more widely known result in part because it can already be explained for a matrix that is distributed with a. The algorithms are much simpler than previously published methods yield better performance and require less work space.

C i C i AB i C i sum_ j0 p-1 A jB ji Since processor i owns C i and B i but not each A j as required by the formula the algorithm will have to send each A j to each processor. Scalable Universal Matrix Multiplication Algorithm For i 0 to nFor j 0 to nFor k 0 to nCij AikBkj Calculates n2 dot products inner products. CiteSeerX - Document Details Isaac Councill Lee Giles Pradeep Teregowda.

The algorithms are much simpler than previously published methods yield better performance and require less work space. The Scalable Universal Matrix Multiplication Algorithm 33 is another algorithm that overcomes all shortcomings of Cannons algorithm and Foxs algorithm. Slow memory references Ω n3 M Hong and Kung 81 Parallel p processors μ Amount of memory needed to store matrices Refs to remote memory.

The PUMMA package includes not only the nontransposed matrix multiplication routine C A B but also transposed multiplication routines C A T B C A B T and C A T B T for a block cyclic data distribution. The algorithms are much simpler than previously published methods yield better performance and require less work. Scalable Universal Matrix Multiplication Algorithm is abbreviated as SUMMA.

Van De Geijn Corresponding Author. Scalable Universal Matrix Multiplication Algorithm listed as SUMMA. The Scalable Universal Matrix Multiplication Algorithm SUMMA is a more practical algorithm that requires less workspace and overcomes the need for a square 2D grid.

For each iteration of k the product of a column vector A times a row vector B is an n-by-n matrix actually just the multiplication table of the elements of the two vectors. On Matrix Multiplication Assume we are using an On3 algorithm Let M Size fast memory cachelocal memory Sequential case. Walker and Jack J.

It is Scalable Universal Matrix Multiplication Algorithm. We believe it is a more widely known result in part because it can already be explained for a matrix that is distributed with a. The algorithm combines storage-optimal matrix-multiplication MatDot codes with the 3D scalable universal matrix multiplication algorithm SUMMA.

Placing k as the outmost loop is the same as expressing C as the sum of n of those multiplication table matrices. Scalable universal matrix multiplication algorithm Concurrency-Practice and Experience 94 1997.

Analysis Of A Class Of Parallel Matrix Multiplication Algorithms