Description of The Method
Suppose we want to solve the following system of linear equations
- Ax = b
for the vector x where the known n-by-n matrix A is symmetric (i.e. AT = A), positive definite (i.e. xTAx > 0 for all non-zero vectors x in Rn), and real, and b is known as well.
We denote the unique solution of this system by .
Read more about this topic: Conjugate Gradient Method
Famous quotes containing the words description of the, description of, description and/or method:
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St. Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)
“Do not require a description of the countries towards which you sail. The description does not describe them to you, and to- morrow you arrive there, and know them by inhabiting them.”
—Ralph Waldo Emerson (1803–1882)
“Whose are the truly labored sentences? From the weak and flimsy periods of the politician and literary man, we are glad to turn even to the description of work, the simple record of the month’s labor in the farmer’s almanac, to restore our tone and spirits.”
—Henry David Thoreau (1817–1862)
“The country needs and, unless I mistake its temper, the country demands bold, persistent experimentation. It is common sense to take a method and try it. If it fails, admit it frankly and try another. But above all, try something. The millions who are in want will not stand idly by silently forever while the things to satisfy their needs are within easy reach.”
—Franklin D. Roosevelt (1882–1945)