Polynomial Multiplication and Fast Fourier Transform
(Com S 477/577 Notes)
Yan-Bin Jia
Oct 21, 2012
Suppose we are given two polynomials:
p(x) = a0 + a1 x + + aN 1 xN 1 ,
q (x) = b0 + b1 x + + bN 1 xN
The Midterm Exam will take place in class on Thursday, Oct 11. It will be a closed-book and closed-notes exam. Scratch papers will be distributed and calculators and drawing tools will be allowed.
The
Com S 477/577 Fall 2012
Assignment 6 (40 pts)
Due before class (hard copy only)
Thursday, October 11
All problems fall within the scope of the Midterm Exam on the due day of this assignment.
1. (9 pts
Parametric Curves
(Com S 477/577 Notes)
Yan-Bin Jia
Oct 2, 2012
1
Introduction
A curve in R2 (or R3 ) is a dierentiable function : [a, b] R2 (or R3 ). The initial point is [a]
and the nal point is [b]
Curvature
(Com S 477/577 Notes)
Yan-Bin Jia
Oct 2, 2012
We want to nd a measure of how curved a curve is. Since this curvature should depend only
on the shape of the curve, it should not be changed wh
Singular Value Decomposition
(Com S 477/577 Notes)
Yan-Bin Jia
Sep 6, 2012
1
Introduction
Now comes a highlight of linear algebra. Any m n matrix can be factored as
A = U V T
where U is an m m orthogo
Solution of Linear Equations
(Com S 477/577 Notes)
Yan-Bin Jia
Sep 4, 2012
We discussed general methods for solving arbitrary equations. We also looked at the special
class of polynomial equations. An
Solution of Nonlinear Equations
(Com S 477/577 Notes)
Yan-Bin Jia
Aug 30, 2010
One of the most frequently occurring problems in scientic work is to nd the roots of equations
of the form
f (x) = 0.
(1)
Roots of Polynomials
(Com S 477/577 Notes)
Yan-Bin Jia
Aug 28, 2012
We will look at how to nd roots, or zeros, of polynomials in one variable. The solution of
multi-variate polynomials can often be tr
Polynomial Interpolation
(Com S 477/577 Notes)
Yan-Bin Jia
Aug 23, 2012
1
Interpolation Problem
Consider a family of functions of a single variable x:
(x; a0 , a1 , . . . , an ),
where a0 , . . . , an
Polynomial Evaluation
(Com S 477/577 Notes)
Yan-Bin Jia
Aug 21, 2012
Polynomials are perhaps the best understood and most applied functions. The foundation comes
from algebra and calculus. Taylors exp
Closed Curves and Space Curves
(Com S 477/577 Notes)
Yan-Bin Jia
Oct 4, 2012
So far we have discussed only local properties of (plane) curves. These properties depend only
on the behavior of a curve n