MATH414.01 ASSIGNMENT 1SOLUTIONS
2.5 Download the file plotfunction1.m from the books web page and execute it. This
should produce two following plots:
The top plot shows the function f (x) = 2 cos(x) ex for 6 x 3, and from
this plot it appears that f (x)
MATH4414.01 ASSIGNMENT 04SOLUTIONS
4.3 Newtons method can be used to compute reciprocals, without division. To compute
1/R, let f (x) = x1 R so that f (x) = 0 when x = 1/R. Write down the Newton
iteration for this problem and compute (by hand or with a ca
MATH4414.01 ASSIGNMENT 06SOLUTIONS
7.4 Assume that a matrix A satisfies P A = LU , where
1 0 0
2 3 1
0 0 1
U = 0 1 2 .
P = 1 0 0
L = 21 1 0
1
1
0 0 2
0 1 0
1
3
4
Use these factors, without forming the matrix A or taking any inverses, to solve the
T
system
MATH4414.01 ASSIGNMENT 02SOLUTIONS
4.2.b Write a routine to use Newtons method or use the routine newton available from
the books web page to find a root of f (x) using initial guess x0 = 5. Print out
your approximate solution xk and the value of f (xk )
MATH4414.01 ASSIGNMENT 03SOLUTIONS
4.1 (a) Write the equation for the tangent line to y = f (x) at x = p.
Solution. The tangent line to y = f (x) at x = p has slope f 0 (p) and so the
equation is
y f (p) = f 0 (p)(x p).
(b) Solve for the x-intercept of th
MATH4414.01 ASSIGNMENT 05SOLUTIONS
5.2 Write down the IEEE double-precision representation for the decimal number 50.2,
using round to nearest.
Solution. Since 50.2 is positive, the sign bit here is s = 0. Also, 25 = 32 50.2 <
26 = 64 so, the exponent is
MATH614
MIDTERM EXAMINATION
1)[25pts]
(a) Define the condition number, (A), for a nonsingular matrix A IR nn , show that (A) 1
and that (AB) (A)(B).
(b) Consider the linear system Ax = b. Let x be the exact solution, and let xc be some
computed approximat
MATH614 FINAL EXAMINATION
Write your full name and answers on the paper provided.
1)[20 pts]
Let A be a given n n nonsingular matrix, and assume a splitting of the form
A = M N, where M is nonsingular. Let x be the solution of the problem Ax = b.
Consider
MATH614
FINAL EXAMINATION
[1] Let
5 1 1
x1
7
1 5 1 x2 = 7
1 1 5
x3
7
Use x(0) = (0, 0, 0)T and compute two iterates of conjugate gradient iteration. Comment
on the results.
[2] (a) Given x = (2, 2, 1)T , find an orthogonal matrix Q such that Qx is paral
MATH614
MIDTERM EXAMINATION
Answer the questions on the paper provided.
1)[25pts]
a) Let v1 = [3, 3, 3, 3]T , v2 = [1, 2, 3, 4]T , and S = spancfw_v1 , v2 IR 4 . Apply GramSchmidt process to S to obtain an orthonormal basis of S. Save the coefficients rj
MATH614 FINAL EXAMINATION
Write your full name and answers on the paper provided.
1)[15pts]
Let A be a given n n nonsingular matrix, and assume a splitting of the form
A = M N, where M is nonsingular. Let x be the solution of the problem Ax = b.
Consider
MATH 614 TEST I
1)[25 pts] (a) Let A be orthogonal matrix. Then find Cond2 (A).
(b) How are Cond2 (A) and Cond2 (A1 ) related? Justify your answer.
(c) How are Cond(cA) and Cond(A) related? Justify your answer.
(d) Prove that Cond(AB) Cond(A)Cond(B) for a
Exam 1
CS424-01/524-01 Fall 2015
Name
The exam is worth 100 points total
You will have 1 hour 20 minutes for the exam
If you leave the classroom, you must turn in your exam.
You may not use a calculator or notes
All answers must be written on the test pap
MATH 614
Test
II
Answer the questions on the paper provided. The exam is one hour and twenty
minutes long.
1)[25pts]
Let v1 = [3, 3, 3, 3]T , v2 = [1, 2, 3, 4]T , and S = spancfw_v1 , v2 IR 22 . Apply Modified
Gram-Schmidt (MGS) process to S to obtain an
MATH614
FINAL EXAMINATION
Write Your Full Name in the Answer Sheet. Answer the questions on the paper
provided.
[1] Let u IR n be a given vector and
P =I
2
uuT
uT u
be a Householder reflector matrix.
(a) Prove that P is orthogonal.
(b) Let x be given and
MATH614
MIDTERM EXAMINATIONII
Answer the questions on the paper provided.
1)[25pts]
a) Let v1 = [3, 3, 3, 3]T , v2 = [1, 2, 3, 4]T , and S = spancfw_v1 , v2 IR 22 . Apply GramSchmidt process to S to obtain an orthonormal basis of S. Save the coefficients
MA 113 - Spring 2016
Homework 1
Name:
Show all work, write clearly, and circle your final answers. All angles should be in radians, not degrees.
1.
(5 pts) Assume that the terminal point of an angle of t radians lies in Q2 and cos(t) = 35 . Find
the other
M3. 120 Fall ZUlb bxam l 3
Part I. Short Answer. On these problems, write your answer in the space below
the problem. Only the answer will be graded, and there is no partial credit. Each
problem is worth three (3) points.
The rst two problems refer to the
Explain what it
means to say that
q) r
b)r
t.)r
d)r
l1m f(x) = 9 and
lim f(x) = I.
x . 2x-2+
As x approaches 2, f(x) approaches
!, but f(2) = 9.
As x approaches 2, f(x) approaches 9, but f(2) = I.
As x approaches 2 from the left, f(x) approaches 9. As x
ENGR 103
Practice Problems
Test #2
Use the following graph for questions 1, 2 & 3. Assume an initial velocity of 1 m/s and an initial
displacement of -2 m.
1. Create the velocity-time and displacement time profiles.
2. What is the velocity at t = 2s? 4s?