An Algorithm for the Vandermonde Matrix-Vector Multiplication with Reduced Multiplicative Complexity

2016 ◽  
pp. 185-194
Author(s):  
Aleksandr Cariow ◽  
Galina Cariowa
Keyword(s):  
Vandermonde Matrix ◽  
Multiplicative Complexity ◽  
Matrix Vector Multiplication ◽  
Matrix Vector

scholarly journals Sparse Matrix-Vector Multiplication on GPGPUs

2017 ◽  
Vol 43 (4) ◽  
pp. 1-49 ◽  
Author(s):  
Salvatore Filippone ◽  
Valeria Cardellini ◽  
Davide Barbieri ◽  
Alessandro Fanfarillo
Keyword(s):  
Sparse Matrix ◽  
Matrix Vector Multiplication ◽  
Matrix Vector

scholarly journals Private and rateless adaptive coded matrix-vector multiplication

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rawad Bitar ◽  
Yuxuan Xing ◽  
Yasaman Keshtkarjahromi ◽  
Venkat Dasari ◽  
Salim El Rouayheb ◽  
...  
Keyword(s):  
Computing Methods ◽  
Erasure Codes ◽  
Time Varying ◽  
New Paradigm ◽  
Matrix Vector Multiplication ◽  
Processing Data ◽  
Computationally Intensive ◽  
Matrix Vector ◽  
Monitoring Devices ◽  
Theoretical Results

AbstractEdge computing is emerging as a new paradigm to allow processing data near the edge of the network, where the data is typically generated and collected. This enables critical computations at the edge in applications such as Internet of Things (IoT), in which an increasing number of devices (sensors, cameras, health monitoring devices, etc.) collect data that needs to be processed through computationally intensive algorithms with stringent reliability, security and latency constraints. Our key tool is the theory of coded computation, which advocates mixing data in computationally intensive tasks by employing erasure codes and offloading these tasks to other devices for computation. Coded computation is recently gaining interest, thanks to its higher reliability, smaller delay, and lower communication costs. In this paper, we develop a private and rateless adaptive coded computation (PRAC) algorithm for distributed matrix-vector multiplication by taking into account (1) the privacy requirements of IoT applications and devices, and (2) the heterogeneous and time-varying resources of edge devices. We show that PRAC outperforms known secure coded computing methods when resources are heterogeneous. We provide theoretical guarantees on the performance of PRAC and its comparison to baselines. Moreover, we confirm our theoretical results through simulations and implementations on Android-based smartphones.

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