MA415
Spring 2008
Midterm 2
Write your full name and answer the question showing all your work on
the problems clearly in the answer sheets provided.
[1] [25pts] Solve the system by nding the P A = LU factorization and then carrying
out the two-step back
x y x
6ppvppwVT
xVpVp~Gvp~p66vGyGppvppwVTVGqxGGpwGG4pqVpppvTp(GpGpGp4vGT6 q
v y y x y x x y y y~ xvrv x w x xr g
p4StuSpux(tv4ve
heheheh
pvpG4cfw_GpvpwTGGw4GXpvGppG4vGVIppyGpu G q
xvr x ~ x y x y y y xv x x y yv xwv s rD
y x x y x ~ z x x
T4pv4VTV84p
MA415
Fall 2010
Midterm Exam
Write your full name and answer the question showing all your work on the
problems clearly in the answer sheets provided.
[1] [20pts] Solve the system by nding the A = LU factorization and then carrying out
the two-step back s
MA415
Spring 2012
Midterm Exam
[1] [20pts] Solve the system by nding the P A = LU factorization and then carrying out
the two-step back substitution.
312
0
x1
6 3 4 x2 = 1
315
x3
3
2[20pts] Consider a function f that satises the following properties:
i)
MATH 415
October 2011
Midterm Examination
Instructions: Show all of your work and write your answers on the answer sheet.
[1] (i) Which of the following xed point iterations will converge faster to 5 (determine this without
computing the iterates):
(a) xn
MA415
Spring 2010
Midterm Exam
Write your full name and answer the question showing all your work on the
problems clearly in the answer sheets provided.
[1] [20pts] Solve the system by nding the P A = LU factorization and then carrying out
the two-step ba
MATH 415
May 2010
Final Examination
Instructions: Show all of your work and write your answers on the answer sheet.
[1] (a) Find the least squares line through the set of data points:
(0, 3), (1, 1), (2, 0), (4, 1), (6, 4)
Answer: 1.1724 + 0.2424x
(b) Fin
MATH 415
Instructions:
Fall 2010
Final Examination
In order to receive full credit, you must show your work and carefully
justify your answers.
Print your name on the answer sheet
You are allowed two hours and thirty minutes for this exam. Please pace
MATH 415
May 2012
Final Examination
Instructions: Show all of your work and write your answers on the answer sheet.
[1] Consider a function f that satises the following conditions:
(a) There exists a root [0, 1].
(b) For all real x, f (x) 2 and 0 f (x) 3.
MATH 415
April 2008
Final Examination
Instructions: Write your name on the answer sheet provided. Show all of your work and
write your answers on the answer sheet. Please box your answers.
[1] (a) Find an approximate formula D(h) for f (x0 ) that uses the