Breaking through memory limitation in GPU parallel processing using Strassen Algorithm

Matrix multiplication is one of the basic operations in linear algebra that mostly used in computer science. For ages, applying naive algorithm to complete it has done it, and it has a standard complexity O(n³). Many researches are concluded to find more efficient and effective algorithm to process this operation, and one day Strassen has one that overcome the naive algorithm complexity with only O(n^2.8074). The basic concept of this algorithm is divide and conquer (DnC) but with adjustment, to break the limitation of memory in a GPU computation. An idea to overcome this limit is to combine CPU and GPU processing, which implement Strassen algorithm. This paper shows the result of breaking through GPU memory limitation, checking the accuracy of the algorithm, compare the running time result and the most important thing is to make sure this algorithm can process bigger matrix than the naive one. Through the created charts and tables based on each performances, it showed that the maximum size of data samples that are processed by Strassen Algorithm reach 32.768 for (2ⁿ×2ⁿ) matrix size, which is bigger than the naive algorithm 8.192 could process. Also for all attempt to matrices with larger than 2048, the running times are way faster, about 0.04 seconds to 0.2 seconds for worst case scenario, and overcome the one with naive algorithm.