# Equal bi-Vectorized (EBV) method to high performance on GPU

## TL;DR

This paper introduces the Equal bi-Vectorized (EBV) method, a GPU-optimized algorithm for LU decomposition that enhances performance through bi-vectorization and vector equalization, suitable for dense and sparse matrices.

## Contribution

The paper presents a novel bi-vectorization and equalization approach to improve LU decomposition efficiency on GPUs, applicable to various parallelism schemes and multi-device setups.

## Key findings

- Demonstrates performance improvements over existing methods
- Effective for both dense and sparse matrices
- Compatible with multiple parallelism strategies

## Abstract

Due to importance of reducing of time solution in numerical codes, we propose an algorithm for parallel LU decomposition solver for dense and sparse matrices on GPU. This algorithm is based on first bi-vectorizing a triangular matrices of decomposed coefficient matrix and then equalizing vectors. So we improve performance of LU decomposition on equal contributed scheme on threads. This algorithm also is convenient for other parallelism method and multi devices. Several test cases show advantage of this method over other familiar method.

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Source: https://tomesphere.com/paper/1907.05767