YOUR NAME:
Midterm, Numerical Analysis, March 3, 2010, with answers.
1. Newtons method for polynomial interpolation works with divided differences f [x0 , x1 , . . . , xk ] for increasing values of k. Here x0 , x1 , . . . , xn
are distinct points on the r
MATHUA.0252, Georg Stadler (NYU Courant)
Spring 2017: Numerical Analysis
Assignment 4 (due Mar. 30, 2017)
1. [1+1pt] Let A Rnn be symmetric.
(a) Proof that all eigenvalues of A are real.
(b) Proof that eigenvectors of A corresponding to different eigenva
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%
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%
Solve the nonlinear equation
2x  tan(x) = 0
using different fixed point iterations
first does not converge, second converges linearly, third converges
quadratically (it's Newton written as fixed point method)
xx = 0:0.01:1.3;
ff = 2*xx  tan(xx
Assignment Set 5, UAMATH02521
Olof Widlund
April 13, 2014
The following assignments are due on April 25 at 12:30pm. No
homework will be accepted after that time. You should give me your
homework in class or put it under my office door (WWH612). Do
not u
Assignment Set 4, UAMATH02521
Olof Widlund
March 31, 2014
The following assignments are due on April 11 at 12:30pm. No
homework will be accepted after that time. You should give me your
homework in class or put it under my office door (WWH612). Do
not u
Assignment Set 3, UAMATH02521
Olof Widlund
March 11, 2014
The following assignments are due on March 28 at 12:30pm. No
homework will be accepted after that time. You should give me your
homework in class or put it under my office door (WWH612). Do
not u
Assignment Set 1, UAMATH02521
Olof Widlund
January 31, 2014
The following assignments are due on February 14 at 12:00 noon.
No homework will be accepted after that time. You should give me
your homework in class or put it under my office door (WWH612).
Assignment Set 2, UAMATH02521
Olof Widlund
February 17, 2014
The following assignments are due on February 28 at 12:00 noon.
No homework will be accepted after that time. You should give me
your homework in class or put it under my office door (WWH612).
Assignment Set 6, UAMATH02521
Olof Widlund
April 24, 2014
The following assignments are due on May 6 at 12:30pm. No
homework will be accepted after that time. You should give me your
homework in class or put it under my office door (WWH612). Do
not use
Numerical Analysis, Midterm, March 6, 2014, with answers.
Cross out what is not meant to be part of your answers.
For full credit motivate your answers.
1. Consider the equation x2 2 = 0.
(a) Starting with x0 = 1 and x1 = 2 compute x2 and x3 using the
bis
YOUR NAME:
Numerical Analysis, Midterm, March 31, 2015.
Cross out what is not meant to be part of your answers.
For full credit motivate your answers.
1. (a) What is the purpose of the Sturm sequence algorithm?
(b) Explain why we can compute the determina
YOUR NAME:
Numerical Analysis, Midterm, March 6, 2012 With Answers.
Cross out what is not meant to be part of your answers.
For full credit motivate your answers.
1. (a) What is Newtons interpolation formula? For what problems is
it used?
(b) How much wor
YOUR NAME:
Numerical Analysis, Quiz # 1, February 16.
With Solutions.
Cross out what is not meant to be part of your answers.
1. Show that the midpoint rule of numerical integration
(b a)f (a + b)/2)
is exact for all linear functions but fails to be so fo
YOUR NAME:
Numerical Analysis, Quiz # 2, February 28.
Cross out what is not meant to be part of your answers.
1. Given an interval [a, b] and a weight function w(x), which is strictly
positive in the open interval (a, b), we can always construct a set of
YOUR NAME:
Numerical Analysis, Quiz # 3, April 10.
Cross out what is not meant to be part of your answers.
1. Consider the equation f (x) = x4 2x3 = 0. We wish to compute
both its roots by using Newtons method with initial guesses suciently close to the r
YOUR NAME:
Numerical Analysis, Quiz # 4, May 1.
Cross out what is not meant to be part of your answers.
1. Consider the double precision oating point numbers each of which
are stored using 64 bits. Of these 11 are used for the exponent and
the rest for th
MATHUA.0252 (Georg Stadler, NYU Courant)
Dongchen Zou
Assignment 2 (Feb. 23, 2017)
1. [2+2+1+1pt] Newtons method computes the new iterate xk+1 as the xintercept of the
line of best fit through the point (xk , f (xk ), i.e., the line that passes through
Numerical Analysis:
Midterm Exam
Spring 2017
Name:
This exam is scheduled for 70 minutes. No calculators, notes or other out
side materials are. permitted. The exam is worth 65 points.

Problem Problem Points
Number Points Earned
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.
. (a
MATHUA
1.
This question is about internal energy and thermal energy (heat).
(a)
Distinguish between internal energy and thermal energy.
.
.
.
.
.
(3)
(b)
Describe, with reference to the energy of the molecules, the difference in internal energy
of a piece of iro