Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 95', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 818 Chapter 18. Integral Equations and Inverse Theory Don t let this notation mislead you into inverting the full matrix W x AS. You only need to solve for some y the linear system W x AS y R and then substitute y into both the numerators and denominators of or . Equations and have a completely different character from the linearly regularized solutions to and . The vectors and matrices in all have size N the number of measurements. There is no discretization of the underlying variable x so M does not come into play at all. One solves a different N x N set of linear equations for each desired value of x. By contrast in one solves an M x M linear set but only once. In general the computational burden of repeatedly solving linear systems makes the Backus-Gilbert method unsuitable for other than one-dimensional problems. How does one choose A within the Backus-Gilbert scheme As already mentioned you can in some cases should make the choice before you see any actual data. For a given trial value of A and for a sequence of x s use equation to calculate q x then use equation to plot the resolution functions b x x as a function of x . These plots will exhibit the amplitude with which different underlying values x contribute to the point u x of your estimate. For the same value of A also plot the function Varp x using equation . You need an estimate of your measurement covariance matrix for this. As you change A you will see very explicitly the trade-off between resolution and stability. Pick the value that meets your needs. You can even choose A to be a function of x A A x in equations and should you desire to do so. This is one benefit of solving a separate set of equations for each x. For the chosen value or values of A you now have a quantitative understanding of your inverse solution procedure. This can prove invaluable if once you are processing real data you need to .
