Hi, I am an experienced software engineer (~14 yrs C++) with MechE background (but never had a job there) and want to get into scientific computing. For first 3 years I did stuff vaguely scicomp but then slipped into pure SW. What would be a good introductory book? (Due to my Engg education, I am familiar with Numerical methods so I seek an advanced introductory book, if that makes sense.)

To be clear, I am not looking for 'recipes' kind of books. I want something more theoretical, though having code in C/C++/Fortran won't hurt. (I want native code, so code in Python, R etc won't help me.)

To clarify about native code, I will be writing native code so I want to be aware of all the precision issues etc, which won't be relevant for code in langs like Python, R, Matlab etc.