CS510 Homework 1 - Solutions
October 5, 2010
Note: Problems graded are I,II,III,VI,VII I. f (x) = x1/2 ,
f (x) = 1 x1/2 2 , f = 1 x3/2 4 ,
3 f (x) = 8 x5/2
(i) P (x) = f (4) + f (4)(x 4) + f (4)(x 4)2 /2
P (x) = 2 + 1 (x 4) 4
(ii) f (5) P (5) = 2 + 1 4
|E
CS 510 Homework - due 10/12/10
I. Using Gaussian elimination with partial pivoting, obtain a P A = LU decomposition of 1 1 2 A = 2 2 1 1 0 2 and use it to solve 1 5. Ax = 4
[You can check your results using matlab command A\b and lu.] II. Obtain a Cholesk
Brief review of linear algebra, plus some additional facts x1 . x= . . xn xi real .
1. Rn
2. A linear combination of vectors x1 , xk in Rn is a vector of the form x = c1 x1 + + ck xk where c1 , ., ck are scalars. 3. A set of vectors cfw_x1 , ., xk is li
import java.util.*;
public class test cfw_
public static void main(String[] args) cfw_
maze x = new maze(101);
for (int i = 0; i < 101; i+) cfw_
for (int j = 0; j < 101; j+) cfw_
/System.out.println(j);
if (j =100) cfw_
if(!x.block[i][j])cfw_
System.out.p
public class cord cfw_
int x;
int y;
public cord(int x,int y)cfw_
this.x=x;
this.y=y;
public void setCoordinates(int x, int y)
cfw_
this.x=x;
this.y=y;
public int getx()cfw_
return this.x;
public int gety()cfw_
return this.y;
import java.util.*;
public class test2 cfw_
public static void main(String[] args) cfw_
maze x = new maze(101);
for (int i = 0; i < 101; i+) cfw_
for (int j = 0; j < 101; j+) cfw_
/System.out.println(j);
if (j =100) cfw_
if(!x.visit[i][j])cfw_
System.out.
Allison Nelson
nelsonam@appstate.edu
(336) 225-6839
http:/themusegarden.wordpress.com
Education
B.S. Computer Science, Magna Cum Laude
Appalachian State University, Boone, NC
University and Departmental Honors, Cumulative GPA: 3.72/4.00
May 2013
Research/
CS 510 Computer Problem: Computation of the roots of a polynomial due 10/5/10
Your objective is to compute the roots (real and complex) of the polynomial p(x) = 18x6 30x5 + 5x4 23x3 + 26x2 9x + 1 to within absolute error 1010 , if possible. Use of Matlab
CS 510 Homework - due 9/28/10 I. (i) Find the Taylor polynomial which matches f (x) = x and its rst two derivatives at x = 4. (ii) Suppose the polynomial in (i) is used to approximate 5. What is the resulting approximation? Bound its absolute error using
import java.util.*;
public class maze cfw_
private int len;
private int sx;
private int sy;
private int tx;
private int ty;
private int size;
private int counter = 0;
private LinkedList<cord> visitstack = new LinkedList<cord>();
private Random rand = new