well-posed problem


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well-posed problem

[′wel ¦pōzd ′präb·ləm]
(mathematics)
A problem that has a unique solution which depends continuously on the initial data.
References in periodicals archive ?
The really profound discoveries in theoretical physics do not begin as well-posed problems. A well-posed problem implies the existence of a theory that provides the language in which to pose the question.
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.
It is possible to consider two well-posed problems for the error field.
The issues of well-posed problems or formal proof are concerns of mathematicians.
Moreover, a computer program can only tackle well-posed problems with the help of an algorithm.