Solution to a well-posed problem. Here we assume that the existence of solutions to a problem has been proven by some method, and one is seeking to construct these solutions.

To give examples that show the failure of technology to solve several well-posed problems that possess (constructive) solutions, and to give examples indicating that widely-used software sometimes provides the wrong answer; and

Instead we concentrate on well-posed problems. In general, the well-posed problems can be divided into two categories, namely, type I and type II.

In this section the crucial and positive effect of technology in constructing the solution of well-posed problems, in particular Type II problems will be surveyed.

Typically, regularization refers to a process wherein an ill-posed problem is replaced by a

well-posed problem. Here, regularization denotes a technique to replace one

well-posed problem by another

well-posed problem that is "easier" to solve.