Solving The Least Squares Problem
The minimum of the sum of squares is found by setting the gradient to zero. Since the model contains m parameters there are m gradient equations.
and since the gradient equations become
- .
The gradient equations apply to all least squares problems. Each particular problem requires particular expressions for the model and its partial derivatives.
Read more about this topic: Least Squares
Famous quotes containing the words solving the, solving, squares and/or problem:
“More than a decade after our fellow citizens began bedding down on the sidewalks, their problems continue to seem so intractable that we have begun to do psychologically what government has been incapable of doing programmatically. We bring the numbers down—not by solving the problem, but by deciding it’s their own damn fault.”
—Anna Quindlen (b. 1952)
“If we parents accept that problems are an essential part of life’s challenges, rather than reacting to every problem as if something has gone wrong with universe that’s supposed to be perfect, we can demonstrate serenity and confidence in problem solving for our kids....By telling them that we know they have a problem and we know they can solve it, we can pass on a realistic attitude as well as empower our children with self-confidence and a sense of their own worth.”
—Barbara Coloroso (20th century)
“An afternoon of nurses and rumours;
The provinces of his body revolted,
The squares of his mind were empty,
Silence invaded the suburbs,”
—W.H. (Wystan Hugh)
“How much atonement is enough? The bombing must be allowed as at least part-payment: those of our young people who are concerned about the moral problem posed by the Allied air offensive should at least consider the moral problem that would have been posed if the German civilian population had not suffered at all.”
—Clive James (b. 1939)