Linear solvers with Tikhonov regularisations

[jwhhh]

Linear solvers initially centred around scipy.linalg.inv

• Case 1 - basic case, $m = (G^TG)^{-1}G^Td$
• Case 2 - basic case with noise, $m = (G^TC_d^{-1}G)^{-1}G^TC_d^{-1}d$
• Case 3 - with zero order Tikhonov, $m = (G^TG + \alpha^2I)^{-1}G^Td$
  • generalised to higher order Tikhonov, $m = (G^TG+\lambda L^TL)^{-1}G^Td$,
• Case 4 - with noise and zero order Tikhonov, $m = (G^T C_d^{-1}G+\alpha^2I)^{-1}G^TC_d^{-1}d$
  • generalised to higher order Tikhonov, $m = (G^TC_d^{-1}G+\lambda L^TL)^{-1}G^TC_d^{-1}d$

Case 3 and 4 yet #TODO

This issue depends on #53