The classic reference on the subject is "Numerical Linear Algebra" by Lloyd Trefethen. Skip to the last chapter on the iterative methods for computational aspects. You'll learn a lot more and faster with Matlab.
AD comes from a different tradition - dating back to FORTRAN 77 programers attempt to differentiate non-elementary functions (For Loops, procedural functions, Subroutines, etc). Note the hardware specs for some nostalgia
https://www.mcs.anl.gov/research/projects/adifor/
https://davidtabora.wordpress.com/wp-content/uploads/2015/01...
A short overview is chapter 11 in Gilbert Strangs's Intro to linear Algebra https://math.mit.edu/~gs/linearalgebra/ila5/linearalgebra5_1...
AD comes from a different tradition - dating back to FORTRAN 77 programers attempt to differentiate non-elementary functions (For Loops, procedural functions, Subroutines, etc). Note the hardware specs for some nostalgia https://www.mcs.anl.gov/research/projects/adifor/