Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm M Nakata, H Nakatsuji, M Ehara, M Fukuda, K Nakata, K Fujisawa The Journal of Chemical Physics 114 (19), 8282-8292, 2001 | 268 | 2001 |

SERIES B: Operations Research M Yamashita, K Katsuki Fujisawa, MN Nakata, M Fukuda, K Kobayashi, ... | 94 | 2010 |

Density matrix variational theory: Application to the potential energy surfaces and strongly correlated systems M Nakata, M Ehara, H Nakatsuji The Journal of chemical physics 116 (13), 5432-5439, 2002 | 91 | 2002 |

Variational calculation of second-order reduced density matrices by strong -representability conditions and an accurate semidefinite programming solver M Nakata, BJ Braams, K Fujisawa, M Fukuda, JK Percus, M Yamashita, ... The Journal of chemical physics 128 (16), 164113, 2008 | 86 | 2008 |

Large-scale semidefinite programs in electronic structure calculation M Fukuda, BJ Braams, M Nakata, ML Overton, JK Percus, M Yamashita, ... Mathematical programming 109 (2-3), 553-580, 2007 | 84 | 2007 |

Latest developments in the SDPA family for solving large-scale SDPs M Yamashita, K Fujisawa, M Fukuda, K Kobayashi, K Nakata, M Nakata Handbook on semidefinite, conic and polynomial optimization, 687-713, 2012 | 75 | 2012 |

PubChemQC project: A large-scale first-principles electronic structure database for data-driven chemistry M Nakata, T Shimazaki Journal of chemical information and modeling 57 (6), 1300-1308, 2017 | 50 | 2017 |

A numerical evaluation of highly accurate multiple-precision arithmetic version of semidefinite programming solver: SDPA-GMP,-QD and-DD. M Nakata 2010 IEEE International Symposium on Computer-Aided Control System Design, 29-34, 2010 | 50 | 2010 |

Strange behaviors of interior-point methods for solving semidefinite programming problems in polynomial optimization H Waki, M Nakata, M Muramatsu Computational Optimization and Applications 53 (3), 823-844, 2012 | 43 | 2012 |

Direct determination of the density matrix using the density equation: Potential energy curves of HF, CH4, BH3, NH3, and H2O M Ehara, M Nakata, H Kou, K Yasuda, H Nakatsuji Chemical physics letters 305 (5-6), 483-488, 1999 | 43 | 1999 |

Direct determination of second-order density matrix using density equation: Open-shell system and excited state M Nakata, M Ehara, K Yasuda, H Nakatsuji The Journal of Chemical Physics 112 (20), 8772-8778, 2000 | 36 | 2000 |

The MPACK (MBLAS/MLAPACK) a multiple precision arithmetic version of BLAS and LAPACK M Nakata http://mplapack. sourceforge. net/, 2010 | 28 | 2010 |

Algorithm 925: Parallel solver for semidefinite programming problem having sparse schur complement matrix M Yamashita, K Fujisawa, M Fukuda, K Nakata, M Nakata ACM Transactions on Mathematical Software (TOMS) 39 (1), 1-22, 2012 | 21 | 2012 |

Size extensivity of the variational reduced-density-matrix method M Nakata, K Yasuda Physical Review A 80 (4), 042109, 2009 | 20 | 2009 |

High-performance general solver for extremely large-scale semidefinite programming problems K Fujisawa, H Sato, S Matsuoka, T Endo, M Yamashita, M Nakata SC'12: Proceedings of the International Conference on High Performance …, 2012 | 18 | 2012 |

The second-order reduced density matrix method and the two-dimensional Hubbard model JSM Anderson, M Nakata, R Igarashi, K Fujisawa, M Yamashita Computational and Theoretical Chemistry 1003, 22-27, 2013 | 16 | 2013 |

Supplementary-light method for measuring the conversion efficiency of multijunction solar cells R Shimokawa, F Nagamine, M Nakata, K Fujisawa, Y Hamakawa Japanese Journal of Applied Physics 28 (5A), L845, 1989 | 16 | 1989 |

SDPA (SemiDefinite Programming Algorithm) and SDPA-GMP User's Manual-Version 7.1. 1 K Fujisawa, M Fukuda, K Kobayashi, M Kojima, K Nakata, M Nakata, ... Research Reports on Mathematical and Computing Sciences, B-448, 2008 | 15 | 2008 |

Relativistic quantum Monte Carlo method using zeroth-order regular approximation Hamiltonian Y Nakatsuka, T Nakajima, M Nakata, K Hirao The Journal of chemical physics 132 (5), 054102, 2010 | 13 | 2010 |

A fast implementation of matrix-matrix product in double-double precision on Nvidia c2050 and application to semidefinite programming M Nakata, Y Takao, S Noda, R Himeno 2012 Third International Conference on Networking and Computing, 68-75, 2012 | 12 | 2012 |