In my presentation, I will present a new approach to numerically solve shell model calculations and complex scaling calculations, which have real energy eigenvalues and complex energy eigenvalues, respectively. For shell model calculations, I have already published in Ref.1 and this new approach works as well as the well-known Lanczos method. In an application concerning to isospin breaking , it is superior to the Lanczos method. I will show this new approach in detail. In the latter part of my presentation, I will show an extension of this work  to complex scaling calculations which is useful to describe resonance states. This approach will be able to open large-scale complex scaling calculations. This work is a result of collaboration with Prof. K. Kaneko, M. Honma, T. Sakurai, Y. Sun, S. Tazaki, G. de Angelis, T. Myo and K. Kato. Reference  T. Mizusaki, K. Kaneko, M. Honma, T. Sakurai, Phys. Rev. C82 024310 (2010).  T. Mizusaki, K, Kaneko, M. Honma, K. Sakurai, Acta Phsica Polonica B 42, 447 (2011). K. Kaneko, T. Mizusaki, Y. Sun, S. Tazaki, G. de Angelis, Phys. Rev. Lett. 109, 092504 (2012).  T.Mizusaki, T.Myo, K.Kato, to be submitted.