chapter  15

Numerical Methods for Large-Scale Electronic State Calculation on Supercomputer

WithTakeo Hoshi, Yusaku Yamamoto, Tomohiro Sogabe, Kohei Shimamura, Fuyuki Shimojo, Aiichiro Nakano, Rajiv Kalia, Priya Vashishta

Computer was invented in the 20th century, and a vast number of numerical algorithms have been developed so far. For example, Francis Sullivan and Jack Dongarra listed up ‘The Top 10 Algorithms’ in the 20th century [55]. Following is the list in chronological order: The Metropolis Algorithm, Simplex Method, Krylov Subspace Method, The Decompositional Approach to Matrix Computations, The Fortran Optimizing Compiler, QR Algorithm, Quicksort, Fast Fourier Transform, Integer Relation Detection, and Fast Multipole Method. Many algorithms in the list are well used in computational physics including nanoscience.