Large Matrix Multiplication Algorithms: Analysis and Comparison

In the realm of computer science and optimization, matrices are fundamental components with a significant role across diverse applications. Matrix multiplication stands as a pivotal operation, and enhancing the efficiency of serial matrix multiplication algorithms holds key importance. This project focuses on optimizing matrix multiplication on a single computing device by exploring algorithmic approaches and optimization techniques. Matrices provide structured data representation, serving purposes ranging from dataset representation, data transformation in computer graphics, image processing, physical system modeling, to mathematical equation solving. This project concentrates specifically on algorithms for matrix multiplication. The standard algorithm computes matrix entries by directly multiplying corresponding input entries, though its efficiency degrades for larger matrices due to its high time complexity. Other algorithms like Strassen's algorithm reduce multiplications or exploit parallelism for efficiency. They employ techniques like divide-and-conquer, fast matrix multiplication, and parallel processing. In this work, these algorithms are analyzed in terms of their concepts, time complexities, and advantages. Practical performance factors like matrix size, hardware architecture, memory needs, cache efficiency, and arithmetic complexity are also explored. Through benchmarking and evaluation on standard platforms, insights into their strengths and weaknesses regarding speed and resource utilization are sought. The ultimate goal is to elevate the efficiency of serial matrix multiplication algorithms in computer science and optimization. By studying and implementing a spectrum of algorithms, the project contributes to optimizing computations and enhancing matrix operation performance across scientific and engineering domains.