As everyone knows.
The regularization theory was originally proposed to solve ill-posed problems.
For a long time, people believed that mathematical problems derived from real-world cases were always well-posed.
Back in the early 20th century,
Hadamard observed a phenomenon:
In quite general situations, solving linear equations can be ill-posed.
Even if the equation has a unique solution, an arbitrarily small disturbance to the right side of the equation can cause a huge change in the solution.
In this context,
If you minimize some norm function of the difference between the two sides, you can't necessarily obtain an approximate solution to the equation.
By the 1960s,
Tikhonov, Ivanov, and Phillips discovered the addition of a regularization term to the error norm function.
That is, regularized norm function rather than solely minimizing error norm, causes the solution sequence to converge toward the correct solution for an ill-posed problem.
In other words,
