This article is composed of two parts; the ultra-large-scale electronic structure theory is reviewed for its fundamental numerical algorithm and its role in nano-material science.
This article is composed of two parts; In the first part (Sec. 1), the ultra-large-scale electronic structure theory is reviewed for (i) its fundamental numerical algorithm and (ii) its role in nano-material science. The second part (Sec. 2) is devoted to the mathematical foundation of the large-scale electronic structure theory and their numerical aspects.