UCLA MATH 151A/2, Friday February 9, 2001
NAME STUDENT ID # This is a closed-book and closed-note examination. No calculators are allowed. Please show all your work. Partial credit will be given to pa
r n l n i r n VU n V#i l rm mdj~ ~j r n l n i n m n ~ n U#i r d md n jml n l n i j n V V n x Fv us ~l lm mmmr ~d~ t r q jd l jld dlj n j ~ ~ n i kUV #kUl n # n i #x e u v y v SVv Uv Ug v v u t x t t u
Final Exam, Math 151A/2, Winter 2001, UCLA, 03/21/2001, 8am-11am I. (a) Let x0 , x1 , ., xn be n + 1 distinct points in [a, b], with x0 = a and xn = b, and f C n+1 [a, b]. Let P (x) = P0,1,.,n(x) be t
Applied Numerical Methods
(MATH 151A, Fall 2016)
Assignment 3
Note:
Due day: Discussion section, 18th October (Tuesday). Assignments handed after the due
date will not be counted.
1. Given that each
Math 151A: Homework 4
Fall 2015
Due: Nov 4, 1pm
All your answers should be submitted in class before class begins (please show your work).
Please make sure to see both sides of this sheet.
1. (a) [15
Math 151A: Homework 5
Fall 2015
Due: Nov 23, 1pm
All your answers except computer programs should be submitted in class before class begins
(please show your work). Computer programs as well as numeri
Applied Numerical Methods
(MATH 151A-Lecture 2, Fall 2017)
Assignment 4
Note:
Due day: 1:50 p.m., Nov 28 (Tuesday). Assignments handed after the due date will not
be counted.
1. Let f (x) be a functi
Applied Numerical Methods
(MATH 151A, Fall 2016)
Assignment 2
Note:
Due day: Discussion section, 11 October (Tuesday). Assignments handed after the due
date will not be counted.
1. Given the followin
Applied Numerical Methods
(MATH 151A-Lecture 2, Fall 2017)
Assignment 3
Note:
Due day: 1:50 p.m., Nov. 14 (Tuesday). Assignments handed after the due date will not
be counted.
1. Let f (x) = 1/x, xi
Applied Numerical Methods
(MATH 151A, Fall 2016)
Assignment 4
Note:
Due day: Discussion section, 25th October (Tuesday). Assignments handed after the due
date will not be counted.
1. (a) Use the Lagr
Final Exam Checklist
Math 151A
June 1, 2016
1. Round-off Errors and Computer Arithmetic
(a) Floating point arithmetic
(b) Machine epsilon
2. Solving Linear Systems
(a) Gaussian Elimination with partia
Math 151A
Midterm Checklist
Midterm 1 Date: Friday, April 22nd , 2016
Note.
You can bring a single-sided letter size of cheat sheet.
Checklist
1. Round-off Errors and Computer Arithmetic
(a) Machine e
Math 151A Applied Numerical Methods
Instructor: Ke Yin
Email: kyin at math dot ucla dot edu
Office: MS 7380
Phone: (310)-825-9369
Webpage: http:/www.math.ucla.edu/~kyin/151a/151a.html
Lectures: MWF 12
MATH 151A Applied Numerical Methods
Fall 2017, Lecture 1
Syllabus
Lecture time:
MWF 10 am 10:50 am
Room:
MS 6229
Website:
https:/ccle.ucla.edu/course/view/17F-MATH151A-1
Instructor:
Alex Austin
Email:
MATH 151A, Fall 2017, Homework 1
Instructor: Alex Austin
Due: Wednesday October 18 (2017) in lecture (10 am).
Midterm type questions
M1. Show that for any positive integers i and j with i > j, we have
Applied Numerical Methods
(MATH 151A, Fall 2016)
Assignment 8
Note:
Due day: Discussion section, 29th November (Tuesday). Assignments handed after the
due date will not be counted.
x
y
1. Let x =
Applied Numerical Methods
(MATH 151A, Fall 2016)
Assignment 7
Note:
Due day: Discussion section, 15th November (Tuesday). Assignments handed after the
due date will not be counted.
1. A function f ha
Fall 2015
Due: Oct 7, 1pm
All your answers except computer programs should be submitted in class before class begins
(please show your work). Computer programs as well as numerical results or plots ge
Math 151A: Homework 3
Fall 2015
Due: Oct 28, 1pm
All your answers should be submitted in class before class begins (please show your work).
p
1. [15 points] Show that kxk2 kxk1 nkxk2 for any vector x
Applied Numerical Methods
(MATH 151A-Lecture 2, Fall 2017)
Assignment 1
Note:
Due day: 1:50 p.m., Oct 17 (Tuesday). Assignments submitted after the due date will
not be accepted.
1. Consider the foll
Lecture 6: Fixed-point Iteration and Newtons Method
1
Fixed-point iteration
Find fixed point of g(x), i.e., g(p) = p.
(1) Choose an initial guess p0 .
(2) Generate cfw_pn = g(pn1 )
n=1 . If pn p as n
Lecture 2: Machine Numbers and Errors
1
Binary Machine Numbers
The standard IEEE 754-2008 defines the set of all machine numbers commonly used by computers,
F (2, 53, 1022, 1024). It uses 64-bit (bina
Lecture 3: Algorithms and Convergence
1
Ways to Reduce Roundoff Errors
I. Avoid subtraction of 2 nearly equal numbers. Reason: it causes cancelation of significant
digits. Given 2 nearly equal numbers
Math 151A
Winter 2016
Homework 3
Due: Friday, Jan 22, 2016.
Reading: Sections 2.2, 2.3.
1. Use Fixed-point Theorem to show that if A > 0, then the sequence defined by
xn =
converges to
A whenever x0 >
Lecture 4: Bisection Method
1
Convergence Rate (cont.)
Definition 1. Let lim F (h) = L, lim G(h) = 0. If there exists K > 0 such that
h0
h0
|F (h) L| K|G(h)|
for sufficiently small h, then we write F
Applied Numerical Methods
(MATH 151A-Lecture 2, Fall 2017)
Assignment 2
Note:
Due date: 1:50 p.m., 31th October (Tuesday). Assignments handed in after the due date
will not be counted.
1. Define the
HW1 Programming problem
First of all, let us define two functions in matlab:
function y=f(x)
y=sin(x)-x;
end
and
function y=fprime(x)
y=cos(x)-1;
end
which means the derivative of the first fu