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 downnot by solving the problem, but by deciding its their own damn fault.”
—Anna Quindlen (b. 1952)
“Will women find themselves in the same position they have always been? Or do we see liberation as solving the conditions of women in our society?... If we continue to shy away from this problem we will not be able to solve it after independence. But if we can say that our first priority is the emancipation of women, we will become free as members of an oppressed community.”
—Ruth Mompati (b. 1925)
“And New York is the most beautiful city in the world? It is not far from it. No urban night is like the night there.... Squares after squares of flame, set up and cut into the aether. Here is our poetry, for we have pulled down the stars to our will.”
—Ezra Pound (18851972)
“I tell you, sir, the only safeguard of order and discipline in the modern world is a standardized worker with interchangeable parts. That would solve the entire problem of management.”
—Jean Giraudoux (18821944)