Are you saying that you want a 1A regulator that will make 12V DC output while the input voltage range is 11 to 16V DC? If so, that device is called a "buck-boost switch-mode power supply or regulator" or "DC to DC converter". It is not a project which lends itself to homebuilding because it uses some rather specialized parts. You would be better off buying one.
You will be paying a high price for making 12V out of 11V when the car battery sags that low. Since that only happens if you have a dead battery (or during cranking while starting the engine), I would not turn on the computer until the engine is running. As soon as the alternator comes on-line, the bus voltage will be 13 to 14.6V, so you could get by with just a "low drop-out linear voltage regulator". These are available inexpensively, and homebuilding is practical.
I use the "power antenna" output from an in-dash stereo receiver to power a 12V to 5V regulator for my XM Roady. It should power the coil of a standard "automotive relay"
like this one.
Wire the "power antenna" lead to terminal 85 (one end of the coil), ground terminal 86 (other end of coil). Connect fused +12V from battery to terminal 30 (common), hook your high-current load to terminal 87.
btw- have you tried your car computer at 11V. I'll bet it will work just fine. In fact, I wondering why a "car computer" wouldn't work over the normal range of voltages encountered in cars; namely from about 9V during cranking to 14.6V when running. All the stuff I have put in my airplane (12V electrical system just like cars) is rated to operate from 11 to 16V.