How can I get 10V (or +5 and -5V) output with at least 100mA output current from a single 9V battery? I couldn't find any suitable IC.

I thought of using a 5V regulator and then using a inverting regulator to get -5V. But 9 - 5 = 4V drop seems very inefficient.

 

why is 9V inefficient, from the datasheet of regulators like the positive and negative ICs 7805 and 7905 (+ve and -ve respectively), inputting a voltage of 7V is good enough to produce the desired output. Why not try it may be using bread-board and give me a feedback I am waiting for you.

 

according to my knowledge, input 9V - output 5V = drop 4V, which is converted into heat. so, it has efficiency of 55% only.
plz, correct me if I am wrong.

 

You will get what you want from a switching boost regulator.

http://www.ti.com/ww/en/simple_switcher_dc_dc_converters/index.html