CS412, Fall 2010
Solutions for Assignment # 2
Prepared by Yimin Tan
October 21, 2010
Problem # 1 (15 points total, with 5 points each method)
1
The problem is basically an implementation practice of Newtons, bisection, and secant method using Matlab.
Choo
CS412, Fall 2013
Solutions for Assignment # 1
Prepared by Yimin Tan
Sep 25, 2013
1
Problem # 1 (15 points)
This is the output obtained after completing the le ck1.m:
> ck1
h(i)
error
-2.5000e-03
1.8482e-05
6.2500e-04
4.6222e-06
1.5625e-04
1.1557e-06
3.906
CS412 Spring Semester 2011
Practice Midterm #1
1. MULTIPLE CHOICE SECTION. Circle or underline the correct answer
(or answers). You do not need to provide a justication for your answer(s).
(1) What would happen if we try to use an N -degree polynomial to
CS412, Fall 2013
Solutions for Assignment # 3
Prepared by Yimin Tan, courtesy of work from Giordano Fusco
October 28, 2013
1
Problem # 1 (10 points)
This question illustrates the diculty one encounters when using the fairly straightforward Vandermonde
app
CS 412 Fall 2011 Solution Key for Assignment 4
Prepared by Brian Nixon from notes by Yimin Tan
December 15, 2011
1
Problem 1
(1) The CEO at your work place, B.E. Late, had scolded Rita for not trying
cubic Hermite interpolation (cf. Assignment 3). She, th
09/05/06
cs412: introduction to numerical analysis
Lecture 1: Introduction
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw
The Essence of Computation
What is computation? This is the most fundamental question in computer science. In o
CS412, Fall 2013
Solutions for Assignment # 2
Prepared by Yimin Tan
October 14, 2013
Problem # 1 (15 points total, with 5 points each method)
1
The problem is an implementation practice of Newtons, bisection, and secant method using Matlab. Choose
any cub
CS412 Spring Semester 2011
Midterm #1 - Solutions to problems
Tuesday 8 March 2010
1. [30% = 5 questions 6% each] MULTIPLE CHOICE SECTION. Circle
or underline the correct answer (or answers). You do not need to provide
a justication for your answer(s).
(1
Chapter 17 Objectives
Recognizing that Newton-Cotes integration
formulas are based on the strategy of replacing a
complicated function or tabulated data with a
polynomial that is easy to integrate.
Knowing how to implement the following single
applicati
Chapter 16 Objectives
Understanding that splines minimize oscillations by fitting
lower-order polynomials to data in a piecewise fashion.
Knowing how to develop code to perform table lookup.
Recognizing why cubic polynomials are preferable to
quadratic
CS412: Lecture #15
Mridul Aanjaneya
March 12, 2015
We shall turn our attention to solving linear equations
Ax = b
where A Rmn , x Rn , b Rm . We already saw examples of methods that
required the solution of a linear system as part of the overall algorithm
CS412: Lecture #3
Mridul Aanjaneya
January 27, 2015
Machine (epsilon)
A concept that is useful in quantifying the error caused by rounding or truncation is the notion of the machine (epsilon). There are a number of (slightly different) definitions in the
CS412: Lecture #16
Mridul Aanjaneya
March 17, 2015
Useful properties of matrix and vector norms
We previously saw that
|Ax| |A| |x|
(1)
for any matrix A, and any vector x (of dimensions mm and m1, respectively).
Note that, when writing an expression such
CS412: Lecture #1
Mridul Aanjaneya
January 20, 2015
Types of Errors
1. When doing integer calculations one can many times proceed exactly,
except of course in certain situations, e.g. division 5/2=2.5. However,
when doing floating point calculations, roun
CS412: Lecture #2
Mridul Aanjaneya
January 22, 2015
Order notation
We say that
f (n) = O(g(n)
read as f is big-oh of g or f is of order g if there is a positive constant C
such that
|f (n)| C|g(n)|
for all n sufficiently large. For example,
2n3 + 3n2 + n
UNIVERSITY OF WISCONSIN - MADISON
Computer Sciences Department
CS412, Fall 16
General Information
September 6, 2016
Course Name:
Introduction to Numerical Methods
Lectures:
Time:
Place:
Instructor:
Name:
Office:
Phone:
e-mail
Office Hours:
TR 12:50-2:15
1
comment concerning the use of the Vandermonde
The objection to the use of the Vandermonde matrix, whether in interpolation or in least squares
approximation, is not that it may have a bad condition number but, rather, that it is the result of the use
of t
CS412: Lecture #7
Mridul Aanjaneya
February 10, 2015
Secant Method
Let the exact solution be a, i.e., f (a) = 0. Define ek = xk a and fk = f (xk ).
Then,
ek+1 = xk+1 a
xk xk1
fk a
fk fk1
(xk1 a)fk (xk a)fk1
fk fk1
ek1 fk ek fk1
fk fk1
ek1 f (a + ek ) ek f
CS412, Fall 06
Prof. Ron
December 19, 2006
Final Exam
The Formul page of cs412s Final Exam, Fall 06
Numerical integration
The numbers j, k are certain integers that differ from one formula to another. Note that the
error for the composite rules are not gi
Intermittent renewable generation and the cost of
maintaining power system reliability
J. Skea, D. Anderson, T. Green, R. Gross, P. Heptonstall and M. Leach
Abstract: There have been attempts, using various approaches, to assess the additional cost of
run
Optimal Economic Power Dispatch in the Presence
of Intermittent Renewable Energy Sources
Salem Elsaiah, Student Member, IEEE, Mohammed Benidris, Student Member, IEEE,
Joydeep Mitra, Senior Member, IEEE, and Niannian Cai, Student Member, IEEE
Department of
CS412: Lecture #14
Mridul Aanjaneya
March 5, 2015
Cubic Hermite Splines
Let us assume a number of x-locations x1 < x2 < . . . < xn and let us make the
hypothesis that we know both f and f 0 at every location xi . We denote these
values by yi = f (xi ) and
CS412: Lecture #6
Mridul Aanjaneya
February 5, 2015
The Bisection method
Newtons method is a popular technique for the solution of nonlinear equations,
but alternative methods exist which may be preferable in certain situations.
The Bisection method is ye
Computational Methods for
Management and Economics
Carla Gomes
Module 8b
The transportation simplex method
The transportation and assignment
problems
Special types of linear programming
problems.
The structure of these problems leads to
algorithms strea
CS412, S16: Assignment 5
April 28, 2016
Due Date: 5/6/2016 11:55pm (100pts)
the problem of computing
Question 1. Lets startwith a discussion of an example. Consider
10. In order to compute 10, we can find a root of f (x) = x2 10. Note that evaluating
f
Introduction to Julia:
Why are we doing this to you?
(Fall 2015)
Steven G. Johnson, MIT Applied Math
MIT classes 18.303, 18.06, 18.085, 18.337
What language for teaching
scientific computing?
For the most part, these are not hard-core programming courses,
CS412: Lecture #11
Mridul Aanjaneya
February 24, 2015
We saw three methods for polynomial interpolation (Vandermonde, Lagrange, Newton). It is important to understand that all three methods compute (in theory) the same exact interpolant Pn (x), just follo
CS412: Lecture #13
Mridul Aanjaneya
March 3, 2015
The Cubic Spline
As always, our goal in this interpolation task is to define a curve s(x) which
interpolates the n data points
(x1 , y1 ), (x2 , y2 ), . . . , (xn , yn )
(where x1 < x2 < . . . < xn )
In th