Parallelizing nested loops on the Intel Xeon Phi on the example of the dense WZ factorization

Bylina, Jarosław; Bylina, Beata

doi:10.15439/2016f436

Cited by 5 publications

(5 citation statements)

References 7 publications

(7 reference statements)

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“…W Z factorization has been applied in modeling of Markov chains aside its parallelization usage [27]. W Z factorization offers parallelization in solving both sparse and dense linear system to enhance performance using OpenMP, GPU, CUDA or EDK HW/SW codesign architecture [28,29,12]. Then, Yalamov [24] presented that W Z factorization is faster on computer with a parallel architecture than any other matrix factorization methods.…”

Section: Importance Of W Z Factorizationmentioning

confidence: 99%

“…Demeure [44] first posited the term hourglass matrix in describing a matrix derived from factorizing a square matrix via quadrant interlocking factorization or bowtie-hourglass factorization. It was further elucidated that hourglass matrix is synonymous to Z-matrix which can be partitioned into blocks structured Z-system [15,28]. Unfortunately, there are changes in structure of Z-matrix from W Z factorization which depend on the type of matrix (Toeplitz, Hankel, Hermitian, centrosymmetric, diagonally dominant or tridiagonal matrix) being factorized.…”

Section: W H Factorizationmentioning

confidence: 99%

See 1 more Smart Citation

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

Bashir

Kamarulhaili

Babarinsa

2023

J. Nig. Soc. Phys. Sci.

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Quadrant Interlocking Factorization (QIF), an alternative to LU factorization, is suitable for factorizing invertible matrix A such that det(A) , 0. The QIF, with its application in parallel computing, is the most efficient matrix factorization technique yet underutilized. The two forms of QIF among others, which are not only similar in algorithm but also in computation, are WZ factorization and WH factorization yet differs in applications and properties. This review discusses both the old form of QIF, called WZ factorization, and the latest form of QIF, called WH factorization, with an example and open questions to further the studies between the two factorization techniques.

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Section: Importance Of W Z Factorizationmentioning

confidence: 99%

Section: W H Factorizationmentioning

confidence: 99%

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

Bashir

Kamarulhaili

Babarinsa

2023

J. Nig. Soc. Phys. Sci.

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“…When parallelizing such cases, it is first necessary to determine at which level of the cycles we want to parallelize, the strategies of which are illustrated in Table 1. [4,7,5,19]…”

Section: Nested Loop Parallelizationmentioning

confidence: 99%

Index Dependent Nested Loops Parallelization with an Even Distributed Number of Steps

Pintér

Szénási

2021

IJCAI

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Parallel processing of algorithms is an effective way to achieve higher performance on multiprocessor systems rather. During parallelization, it is critical to minimize the difference between the processing time for threads. It is necessary to choose a method that can efficiently distribute the workload evenly across the threads. This paper deals with a special kind of nested loops where the internal loop iterator depends on the outer loop iterator. In such cases, the process can be represented as an upper (or lower) triangular matrix. This paper introduces a method for partitioning the outer loop according to the indices in an almost optimal manner, so that the partial loops in each thread will take nearly the same number of steps. In addition, we examine the potential of a perfect partition and try to determine the maximum (but still meaningful) partition size.Povzetek: Predstavljena je metoda paralelizma za posebno vrsto vgnezdenih zank.

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“…• wz -WZ factorization: dense, square, non-structured matrix factorization algorithm [20], • edge detect -2D-convolution routine to expose edge information from the UTDSP Benchmark suite 8 ,…”

Section: Experimental Studymentioning

confidence: 99%

Optimizing Numerical Code by means of the Transitive Closure of Dependence Graphs

Palkowski

Bielecki

2017

Annals of Computer Science and Information Systems

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Abstract-A challenging task in numerical programming modern computer systems is to effectively exploit the parallelism available in the architecture and manage the CPU caches to increase performance. Loop nest tiling allows for both coarsening parallel code and improving code locality. In this paper, we explore a new way to generate tiled code and derive the free schedule of tiles by means of the transitive closure of loop nest dependence graphs. Multi-threaded code executes tiles as soon as their operands are available. To design the approach, loop dependences are presented in the form of tuple relations. Discussed techniques are implemented in the source-to-source TRACO compiler. Experimental study, carried out on multi-core architectures, demonstrates the considerable speed-up of tiled numerical codes generated by the presented approach.

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Parallelizing nested loops on the Intel Xeon Phi on the example of the dense WZ factorization

Cited by 5 publications

References 7 publications

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

Index Dependent Nested Loops Parallelization with an Even Distributed Number of Steps

Optimizing Numerical Code by means of the Transitive Closure of Dependence Graphs

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