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:
“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)
“Cultural expectations shade and color the images that parents- to-be form. The baby product ads, showing a woman serenely holding her child, looking blissfully and mysteriously contented, or the television parents, wisely and humorously solving problems, influence parents-to-be.”
—Ellen Galinsky (20th century)
“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 (1885–1972)
“The writer operates at a peculiar crossroads where time and place and eternity somehow meet. His problem is to find that location.”
—Flannery O’Connor (1925–1964)