Information technology has transformed our world as an innovation enabler in our daily lives on how we interact with the world and people around us. One of the key driver for this innovation is the exponential growth of computational capability – over the last seventy years starting from ENIAC and then followed with Moore’s law exponent growth. Along with exponential growth of computer hardware, algorithms and methods have also progressed to solve complex science and technology applications that can take advantage of evolving generation of computer hardware. One can easily argue that mathematical algorithms from interdisciplinary sciences played significant role as key enablers for information sciences and information technology revolution. In this talk, we will review key mathematical algorithmic research that played key role over the last 70 years in our evolving computing hardware era - ENIAC, digital computing, vector computing, massively parallel computing, cloud computing, multi-core computing, and mobile computing. Next, we will discuss algorithmic research challenges for future computing hardware that is envisioned to be heterogeneous or hybrid computing consisting of vector computing processors, multi-core computing processors, neuromorphic computing processors, mobile tactical cloudlets, and quantum computing processors with software based intelligent networking as backbone.
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