Researchers from the Universitat Politècnica de València (UPV) have discovered a faster and more precise method for calculating matrix functions, which represents a revolution in the field of mathematics that allows us to leave behind a system that has been unbeatable for 50 years.
The High Performance Scientific Computing group of the UPV has developed this new method, which, as sources from the university institution explained to Efe, has numerous applications in science and engineering.
Since the 1970s, the international scientific community had ruled out polynomial approximations to calculate matrix functions, but now these UPV researchers have shown that they can be more efficient and precise than rational approximations, the most widely used to date. moment.
Their work leaves behind the system used for half a century to calculate matrix polynomials and polynomial approximations, devised by researchers Larry Stockmeyer, from the Massachusetts Institute of Technology, and Michael Paterson, from the University of Warwick.
To calculate matrix functions, UPV researchers have developed algorithms that are faster and more precise than existing ones, and have obtained general formulas to further reduce the computational cost.
Matrix functions have numerous applications in fields such as robotics and artificial intelligence, through quantum mechanics, quantum chemistry, network connectivity, economics or aeronautics, among others.
As Jorge Sastre, one of the founders of the UPV’s High Performance Scientific Computing Group (HiPerSc) explained, “Paterson and Stockmeyer contributed with their proposal to facilitate the calculation of matrix polynomials, a really expensive operation. Their work has “It has been and is fundamental in multiple fields. Now, our work allows us to go a step further than what these researchers took in 1973, further accelerating these calculations.”
“After almost 50 years we have shown that polynomial approximations can be more efficient than rational ones, and they are also giving more precise results in the various cases in which we are applying them”, highlighted Sastre, for whom “this is the future of matrix functions, since with these many problems of physics, economics, chemistry or biology can be solved more efficiently”.
Researchers from the High Performance Scientific Computing group at the UPV continue to work in this field to continue improving the methods for calculating matrix functions and exploring new practical applications.
“This discovery is yet another example of the potential of scientific research to improve our understanding of the world and solve complex problems,” the researcher concluded.
