# On the Design, Development, and Analysis of Optimized Matrix-Vector Multiplication Routines for Coprocessors

## Abstract

The manycore paradigm shift, and the resulting change in modern computer architectures, has made the development of optimal numerical routines extremely challenging. In this work, we target the development of numerical algorithms and implementations for Xeon Phi coprocessor architecture designs. In particular, we examine and optimize the general and symmetric matrix-vector multiplication routines (gemv/symv), which are some of the most heavily used linear algebra kernels in many important engineering and physics applications. We describe a successful approach on how to address the challenges for this problem, starting with our algorithm design, performance analysis and programing model and moving to kernel optimization. Our goal, by targeting low-level and easy to understand fundamental kernels, is to develop new optimization strategies that can be effective elsewhere for use on manycore coprocessors, and to show significant performance improvements compared to existing state-of-the-art implementations. Therefore, in addition to the new optimization strategies, analysis, and optimal performance results, we finally present the significance of using these routines/strategies to accelerate higher-level numerical algorithms for the eigenvalue problem (EVP) and the singular value decomposition (SVD) that by themselves are foundational for many important applications.

- Authors:

- University of Tennessee (UT)
- ORNL

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1261482

- DOE Contract Number:
- AC05-00OR22725

- Resource Type:
- Book

- Resource Relation:
- Journal Volume: 9137

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Kabir, Khairul, Haidar, Azzam, Tomov, Stanimire, and Dongarra, Jack J.
```*On the Design, Development, and Analysis of Optimized Matrix-Vector Multiplication Routines for Coprocessors*. United States: N. p., 2015.
Web. doi:10.1007/978-3-319-20119-1_5.

```
Kabir, Khairul, Haidar, Azzam, Tomov, Stanimire, & Dongarra, Jack J.
```*On the Design, Development, and Analysis of Optimized Matrix-Vector Multiplication Routines for Coprocessors*. United States. doi:10.1007/978-3-319-20119-1_5.

```
Kabir, Khairul, Haidar, Azzam, Tomov, Stanimire, and Dongarra, Jack J. Thu .
"On the Design, Development, and Analysis of Optimized Matrix-Vector Multiplication Routines for Coprocessors". United States.
doi:10.1007/978-3-319-20119-1_5.
```

```
@article{osti_1261482,
```

title = {On the Design, Development, and Analysis of Optimized Matrix-Vector Multiplication Routines for Coprocessors},

author = {Kabir, Khairul and Haidar, Azzam and Tomov, Stanimire and Dongarra, Jack J},

abstractNote = {The manycore paradigm shift, and the resulting change in modern computer architectures, has made the development of optimal numerical routines extremely challenging. In this work, we target the development of numerical algorithms and implementations for Xeon Phi coprocessor architecture designs. In particular, we examine and optimize the general and symmetric matrix-vector multiplication routines (gemv/symv), which are some of the most heavily used linear algebra kernels in many important engineering and physics applications. We describe a successful approach on how to address the challenges for this problem, starting with our algorithm design, performance analysis and programing model and moving to kernel optimization. Our goal, by targeting low-level and easy to understand fundamental kernels, is to develop new optimization strategies that can be effective elsewhere for use on manycore coprocessors, and to show significant performance improvements compared to existing state-of-the-art implementations. Therefore, in addition to the new optimization strategies, analysis, and optimal performance results, we finally present the significance of using these routines/strategies to accelerate higher-level numerical algorithms for the eigenvalue problem (EVP) and the singular value decomposition (SVD) that by themselves are foundational for many important applications.},

doi = {10.1007/978-3-319-20119-1_5},

journal = {},

number = ,

volume = 9137,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}