Homework assignment 8:
Suppose your background assumptions B are such that your degree of belief that an arbitrary
object a is not white is lower than your degree of belief that a is a swan say, becau
Homework assignment 7:
Consider two objects, today and tomorrow, and one property they can have, whether or not the
sun rises on them. There are four possibilities:
s1 = the sun rises today and the su
Homework assignment 4:
A partition P of an arbitrary non-empty set W is a set of subsets of W, P (W), such that any
two members B and C of P are mutually exclusive (have no members in common), B C = ,
Homework assignment 3:
The strong party-hypothesis says that everybody who had time attended the party. The weak party
hypothesis says that somebody had time and attended the party. Parisa, Seya, and
Homework assignment 2:
The swan-hypothesis H is a universal if-then sentence and says that all swans are white. H is
logically equivalent to the universal if-then sentence H that everything that is no
Homework assignment 1:
Intuitively, a set is a collection of objects (things, entities). For instance, the set T of people
teaching this course is the collection of objects (or subjects, if you prefer
Q UESTION 3 Construct a polynomial of degree at most 3 that interpolates (0, 1), (1, 3), (3, 13). Is it
CSC336 Tutorial 8 Interpolation
Q UESTION 1 Construct a polynomial of degree at most 2 that inte
Q UESTION 2 Determine a, b, c and d so that the piecewise cubic polynomial
(x) = 1 + 2 x x3
S0
if 0 x < 1
S (x) =
1(x) = a + b(x 1)+ c(x 1)2 + d(x 1)3 if 1 x 2
S
CSC336 Tutorial 9 Splines
Q UESTION
Applying (2) to both triples of method (e), we get p = 2 (quadratic conv.). Applying (1) to all three
CSC336 Tutorial 7 Nonlinear equations
Q UESTION 1 Assume that ve iterative methods applied to a no
CSC336 Tutorial 4 GE/LU, pivoting, scaling
Q UESTION 2 Do the same as in Question 1 with partial (row) pivoting. Furthermore, indicate the
pivotal vector ipiv at each step of GE, the elementary permut
CSC336 Tutorial 5 Norms and condition numbers
Q UESTION 2 Let A =
Ax
x
Q UESTION 1 Prove that maxx=0
= max cfw_ Ax
x =1
(DA).
PROOF:
ANSWER: We have A
Also,
Ax
x
Ax
2. Note that max
= max A
= max
x=
CSC336 Tutorial 2 Computer arithmetic
Q UESTION 1 Find the positive numbers in R2(4, 3) assuming normalized mantissa.
ANSWER: The numbers in R2(4, 3) are of the form f 2e, where f the mantissa and e t
CSC336 Tutorial 3 Matrices, operation counts, GE/LU
Q UESTION 3 Show that the inverse of a l.t. matrix is a l.t. matrix.
Q UESTION 1 Show that the product of lower triangular (l.t.) matrices is a lowe
CSC336S
Assignment 3
Due Wednesday, April 3, 2013, 6:10 PM
No late assignments (even with penalty) will be accepted. Please write your family and given names and underline your
family name on the fron
CSC336S
Assignment 2
Due Monday, March 11, 2013
Please write your family and given names and underline your family name on the front page of your paper.
General note: Plotting quantity y versus quanti
CSC336S
Assignment 1
Due Monday, February 4, 2013
Please write your family and given names and underline your family name on the front page of your paper.
1.
(a)
[10 points] Find the condition number
Piecewise polynomials and splines
Piecewise polynomials and splines - dimension of pp space
Let = cfw_ a = x 0 , x 1 , . . . , x n = b be a set of distinct points, called knots or nodes or
breakpoints
Polynomial interpolation with Lagrange basis
Polynomial interpolation with Lagrange basis
We (again) construct a polynomial p n ( x ) of degree at most n, that interpolates the data
( x i , f i ), i =