Homework Answers
A) Spline interpolation consists of a approximation of a function by means of series of polynomials over adjacent intervals with contin atuat enddend point of intervals .
Therefore spline function is a smoothing interpolation.
True.
B) Given cos(n arccosx) is polynomial of degree 1 but not n.
False.
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Q4 Spline 5 Points A spline function is a smooth interpolation. O True O False Q5...
Q2 5 Points Interpolation is the process of finding and evaluating a differentiable function whose graph...
Q2 5 Points Interpolation is the process of finding and evaluating a differentiable function whose graph goes through a set of given points. True O False Q3 Divided 5 Points Divided differences are invariant under the permutation of the indexes of the data set. True O False Q4 Spline 5 Points A spline function is a smooth interpolation. True False Q5 Polynomial 5 Points For 15x< 1 the expression cos(n arccosa) is a polynomial of degree n. True O False...
TRUE OR FALSE numeric analysis subject TRUE OR FALSE a) Interpolation is the proccess of finding...
TRUE OR FALSE
numeric analysis subject
TRUE OR FALSE a) Interpolation is the proccess of finding and evaluating a differientable function whose graph goes through a set of given points. b) Divided differences are invariant under the permutation of the indexes of the data set. c) A spline function is a smooth interpolation d) For -1 LX 41 the expression (narccos x) is a polynomial of degree n.
TRUE OR FALSE numeric analysis subject 6) Divided differences are invariant under the permutation of the...
TRUE OR FALSE
numeric analysis subject
6) Divided differences are invariant under the permutation of the indexes of the data set. (c) A spline function is a smooth interpolation d) For -1 2x1 the expression (narccos x) is a polynomial of degree n. e) Simpson's rule uses a quadratic interpolation of a function on a closed interval
Q10 General 15 Points Find the solution to the interpolation problem of finding a polynomial q(x)...
Q10 General 15 Points Find the solution to the interpolation problem of finding a polynomial q(x) with deg(q) < 2 and such that q(X) = Yo, q(x1) = yi, and q' (x1) = yi with Xo <31. Under what exact conditions is deg(q) = 2?
Q8 Spline 15 Points Define s(2) = -5 + 8x6x2 + 2x2 on 1 < x...
Q8 Spline 15 Points Define s(2) = -5 + 8x6x2 + 2x2 on 1 < x <2, and 8(x) = 27 402 + 1822. on 2<< <3 Verify that s() is a cubic spline function on (1,3). Is it a natural spline function on this interval?
Q10 General 15 Points Find the solution to the interpolation problem of finding a polynomial q(x)...
Q10 General 15 Points Find the solution to the interpolation problem of finding a polynomial q(x) with deg(q) < 2 and such that 9(20) = yo 9(x1) = y1, and q'(x1) = y1 with x0 < 21. Under what exact conditions is deg(q) = 2? Please select file(s) Select file(s) Submit & View Submission>
Question 1 2 pts The Hermite Interpolation polynomial for 33 distinct nodes has Degree at most...
Question 1 2 pts The Hermite Interpolation polynomial for 33 distinct nodes has Degree at most {Be Careful with the answer. Look at the Theorem and the Question Carefully; compare the given information} Question 2 2 pts If f € C4 [a, b] and p1, P2, P3, and p4 are Distinct Points in [a, b], Then 1. There are two 3rd divided differences 2. There is exactly one 3rd divided difference and it is equal to the value of f(iv)...
If n<30, we cannot perform a hypothesis test for Ho:p = 0.5. O True O False
If n<30, we cannot perform a hypothesis test for Ho:p = 0.5. O True O False
beta is 1 2. ( 20p.) Consider the cubic spline for a function f on (0,...
beta is 1
2. ( 20p.) Consider the cubic spline for a function f on (0, 2) defined by 223 + ax2 + rx + 1 if 0 < x < 1 S(X) = (.x - 1)3 + c(x - 1)2 + d(x - 1) + B if i < x < 2 S(x) = { where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
Q2 5 Points Interpolation is the process of finding and evaluating a differentiable function whose graph...
Q2 5 Points Interpolation is the process of finding and evaluating a differentiable function whose graph goes through a set of given points. O True O False Q3 Divided 5 Points Divided differences are invariant under the permutation of the indexes of the data set. O True O False
Q2 5 Points Interpolation is the process of finding and evaluating a differentiable function whose graph goes through a set of given points. True O False Q3 Divided 5 Points Divided differences are invariant under the permutation of the indexes of the data set. True O False Q4 Spline 5 Points A spline function is a smooth interpolation. True False Q5 Polynomial 5 Points For 15x< 1 the expression cos(n arccosa) is a polynomial of degree n. True O False...
TRUE OR FALSE
numeric analysis subject
TRUE OR FALSE a) Interpolation is the proccess of finding and evaluating a differientable function whose graph goes through a set of given points. b) Divided differences are invariant under the permutation of the indexes of the data set. c) A spline function is a smooth interpolation d) For -1 LX 41 the expression (narccos x) is a polynomial of degree n.
TRUE OR FALSE
numeric analysis subject
6) Divided differences are invariant under the permutation of the indexes of the data set. (c) A spline function is a smooth interpolation d) For -1 2x1 the expression (narccos x) is a polynomial of degree n. e) Simpson's rule uses a quadratic interpolation of a function on a closed interval
Q10 General 15 Points Find the solution to the interpolation problem of finding a polynomial q(x) with deg(q) < 2 and such that q(X) = Yo, q(x1) = yi, and q' (x1) = yi with Xo <31. Under what exact conditions is deg(q) = 2?
Q8 Spline 15 Points Define s(2) = -5 + 8x6x2 + 2x2 on 1 < x <2, and 8(x) = 27 402 + 1822. on 2<< <3 Verify that s() is a cubic spline function on (1,3). Is it a natural spline function on this interval?
Q10 General 15 Points Find the solution to the interpolation problem of finding a polynomial q(x) with deg(q) < 2 and such that 9(20) = yo 9(x1) = y1, and q'(x1) = y1 with x0 < 21. Under what exact conditions is deg(q) = 2? Please select file(s) Select file(s) Submit & View Submission>
Question 1 2 pts The Hermite Interpolation polynomial for 33 distinct nodes has Degree at most {Be Careful with the answer. Look at the Theorem and the Question Carefully; compare the given information} Question 2 2 pts If f € C4 [a, b] and p1, P2, P3, and p4 are Distinct Points in [a, b], Then 1. There are two 3rd divided differences 2. There is exactly one 3rd divided difference and it is equal to the value of f(iv)...
If n<30, we cannot perform a hypothesis test for Ho:p = 0.5. O True O False
beta is 1
2. ( 20p.) Consider the cubic spline for a function f on (0, 2) defined by 223 + ax2 + rx + 1 if 0 < x < 1 S(X) = (.x - 1)3 + c(x - 1)2 + d(x - 1) + B if i < x < 2 S(x) = { where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
Q2 5 Points Interpolation is the process of finding and evaluating a differentiable function whose graph goes through a set of given points. O True O False Q3 Divided 5 Points Divided differences are invariant under the permutation of the indexes of the data set. O True O False
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