![14. Let so(z) = 1+c(x+1)3 for-1 < z < 0 for some real constant c. Determine s1() for 0 S 1 such that so(x) s1() for 0S for-1 < x < 0; s(x) = 1 is a natural cubic spline on [-1, 1] with nodes at 1,0,1. How must c be chosen if one wants s(1) =-1?](http://img.homeworklib.com/questions/8d76a410-bf86-11ea-b3fc-43f30fb95b2c.png?x-oss-process=image/resize,w_560)
Homework Answers
Add Answer to:
14. Let so(z) = 1+c(x+1)3 for-1 < z < 0 for some real constant c. Determine...
Homework Problem Set 16 x-1)3 for 0 sx$1 a cubic spline? 1. Is the function s (x) = {2(-1)3 for 1...
Homework Problem Set 16 x-1)3 for 0 sx$1 a cubic spline? 1. Is the function s (x) = {2(-1)3 for 1 < x 2 -5 +8x-6x2 2x3 for1 sx s 2 Is the function s(x)-[ natural? Let x for j 1,2,3,4 by a calculation on paper 3 a cubic spline? Is it [1,0,1,0]. Determine the natural spline s with s(y)-yi 2. 18x2-2x3 for 2
0.19 0.. 1. (Natural Splines) Find the natural cubic spline S(x) satisfying S(0) = 0, S(1/2)...
0.19 0.. 1. (Natural Splines) Find the natural cubic spline S(x) satisfying S(0) = 0, S(1/2) = 1, S(1) = 0. Your answer will be 2 cubic polynomials, S.(x), S1(x). Verify that your answer satisfies all the necessary conditions (interpolation, continuity of 1st and 2nd derivatives, boundary conditions). We were unable to transcribe this image
Determine the value of the coefficients a, b, c, d and e so that the following...
Determine the value of the coefficients a, b, c, d and e so that the following f(a) is a natural cubic spline on (0,2]; 3 € [0, 1], c+ d(- 1) + (x - 2)2 + (x - 2) 3€ [1, 2] f(x) = {1+2-3 + bx3
Problem 4 Let f(x) be a cubic polynomial defined on interval [−1, 1]. Determine a Gaussian interg...
Problem 4 Let f(x) be a cubic polynomial defined on interval
[−1, 1]. Determine a Gaussian intergration formula with minimal
number of nodes such that the integral formula Xn i=0 f(xi)wi is
exact for cubic polynomials.
Problem 4 Let f(z) be a cubic polynomial defined on interval [-1,. Determine a Gaussian intergration formula with minimal number of nodes such that the integral formula is exact for cubic polynomials.
Problem 4 Let f(z) be a cubic polynomial defined on interval [-1,....
complex analysis Let f(z) be continuous on S where for some real numbers 0< a <...
complex analysis
Let f(z) be continuous on S where for some real numbers 0< a < b. Define max(Re(z)Im(z and suppose f(z) dz = 0 S, for all r E (a, b). Prove or disprove that f(z) is holomorphic on S.
Suppose f : B(0.1) C is holomorphic, with irg:) 1 for every z є B(0,1). Suppose also that f(0)-0, so f(z)g(2) for some holomorphic function g: B(0,1)C. (a) By applying the Maximum Principle to g on B...
Suppose f : B(0.1) C is holomorphic, with irg:) 1 for every z є B(0,1). Suppose also that f(0)-0, so f(z)g(2) for some holomorphic function g: B(0,1)C. (a) By applying the Maximum Principle to g on B(0, r) where 0 < r < 1 , deduce that If( S for every 2E (0, 1) . (b) Show also that |f'(0) S1 (c) Show that if lf(z)- for some z B(0,1)\(0), or if If,(0)| = 1 , then there is a...
6. Consider f(x)-sinx and evenly spaced nodes 0-0 < xīく… < Zn-2T. Let P(z) be the piecewise cubic interpolant given values and first derivatives of f at the nodes. (a) In the case n = 100, use...
6. Consider f(x)-sinx and evenly spaced nodes 0-0 < xīく… < Zn-2T. Let P(z) be the piecewise cubic interpolant given values and first derivatives of f at the nodes. (a) In the case n = 100, use calculus and the error formula 4! where 1 E [xi,Ti+1], to bound the absolute error lf(1)-P(1) (b) For arbitrary x E [0.2 , use error bounds to determine n ensuring that If(x)- P(x) s 10-10
6. Consider f(x)-sinx and evenly spaced nodes 0-0
)-( 1 (c) Let C be a real 3 x 3 matrix and b be a...
)-( 1 (c) Let C be a real 3 x 3 matrix and b be a real 3-vector. The general solution to the matrix equation Cx=b is given by 2 2 =X3 + -4 2 for all XER Let 10 y = -6 8 (i) Let z be a real 3-vector. Find the solution set to the matrix equation Cz=0 (ii) Calculate M1, M2 ER such that 2 y = M1 ( 3 + H2 ·()--() 1 (iii) Express Cy...
13. Let W = {ī E R4 : Ai = 0} for some constant matrix A....
13. Let W = {ī E R4 : Ai = 0} for some constant matrix A. Suppose all solutions are 1 ES1 lo 1 +r , where t,s,r can be any real numbers. Let S = 0 1 'lo (a) (3 pts) What must the dimensions of the matrix A be? Justify briefly. (b) (8 pts) Show directly from the definition that S is a linearly independent set. (c) (6 pts) Without doing any further) computations, explain why S is...
Let Z ∼ N(0, 1). Find a constant c for which P(Z ≥ c) = 0.1587....
Let Z ∼ N(0, 1). Find a constant c for which P(Z ≥ c) = 0.1587. Round the answer to two decimal places. Find a constant c for which P(c ≤ Z ≤ 0) = 0.4772. Round the answer to two decimal places. Find a constant c for which P(−c ≤ Z ≤ c) = 0.8664. Round the answer to two decimal places. Find a constant c for which P(0 ≤ Z ≤ c) = 0.2967. Round the answer to...
Homework Problem Set 16 x-1)3 for 0 sx$1 a cubic spline? 1. Is the function s (x) = {2(-1)3 for 1 < x 2 -5 +8x-6x2 2x3 for1 sx s 2 Is the function s(x)-[ natural? Let x for j 1,2,3,4 by a calculation on paper 3 a cubic spline? Is it [1,0,1,0]. Determine the natural spline s with s(y)-yi 2. 18x2-2x3 for 2
0.19 0.. 1. (Natural Splines) Find the natural cubic spline S(x) satisfying S(0) = 0, S(1/2) = 1, S(1) = 0. Your answer will be 2 cubic polynomials, S.(x), S1(x). Verify that your answer satisfies all the necessary conditions (interpolation, continuity of 1st and 2nd derivatives, boundary conditions). We were unable to transcribe this image
Determine the value of the coefficients a, b, c, d and e so that the following f(a) is a natural cubic spline on (0,2]; 3 € [0, 1], c+ d(- 1) + (x - 2)2 + (x - 2) 3€ [1, 2] f(x) = {1+2-3 + bx3
Problem 4 Let f(x) be a cubic polynomial defined on interval
[−1, 1]. Determine a Gaussian intergration formula with minimal
number of nodes such that the integral formula Xn i=0 f(xi)wi is
exact for cubic polynomials.
Problem 4 Let f(z) be a cubic polynomial defined on interval [-1,. Determine a Gaussian intergration formula with minimal number of nodes such that the integral formula is exact for cubic polynomials.
Problem 4 Let f(z) be a cubic polynomial defined on interval [-1,....
complex analysis
Let f(z) be continuous on S where for some real numbers 0< a < b. Define max(Re(z)Im(z and suppose f(z) dz = 0 S, for all r E (a, b). Prove or disprove that f(z) is holomorphic on S.
Suppose f : B(0.1) C is holomorphic, with irg:) 1 for every z є B(0,1). Suppose also that f(0)-0, so f(z)g(2) for some holomorphic function g: B(0,1)C. (a) By applying the Maximum Principle to g on B(0, r) where 0 < r < 1 , deduce that If( S for every 2E (0, 1) . (b) Show also that |f'(0) S1 (c) Show that if lf(z)- for some z B(0,1)\(0), or if If,(0)| = 1 , then there is a...
6. Consider f(x)-sinx and evenly spaced nodes 0-0 < xīく… < Zn-2T. Let P(z) be the piecewise cubic interpolant given values and first derivatives of f at the nodes. (a) In the case n = 100, use calculus and the error formula 4! where 1 E [xi,Ti+1], to bound the absolute error lf(1)-P(1) (b) For arbitrary x E [0.2 , use error bounds to determine n ensuring that If(x)- P(x) s 10-10
6. Consider f(x)-sinx and evenly spaced nodes 0-0
)-( 1 (c) Let C be a real 3 x 3 matrix and b be a real 3-vector. The general solution to the matrix equation Cx=b is given by 2 2 =X3 + -4 2 for all XER Let 10 y = -6 8 (i) Let z be a real 3-vector. Find the solution set to the matrix equation Cz=0 (ii) Calculate M1, M2 ER such that 2 y = M1 ( 3 + H2 ·()--() 1 (iii) Express Cy...
13. Let W = {ī E R4 : Ai = 0} for some constant matrix A. Suppose all solutions are 1 ES1 lo 1 +r , where t,s,r can be any real numbers. Let S = 0 1 'lo (a) (3 pts) What must the dimensions of the matrix A be? Justify briefly. (b) (8 pts) Show directly from the definition that S is a linearly independent set. (c) (6 pts) Without doing any further) computations, explain why S is...
Most questions answered within 3 hours.
-
5. Discuss the use of fault tree analysis (FTA) for risk
assessment (maximum one paragraph).
asked 18 minutes ago -
Given that a sample of aluminium oxide has a Young's modulus of
393 GPa and a...
asked 1 hour ago -
At a certain temperature, the equilibrium constant, Kc, for this
reaction is 53.3.
H2(g)+I2(g)−⇀↽−2HI(g)Kc=53.3
At this...
asked 3 hours ago -
Question1 ) The STL provides similiar classes called stack and
queue, both of which gave functions...
asked 4 hours ago -
For Questions 1-4, assume you have 5 bits available:
1. For (positive) integers: What is the...
asked 4 hours ago -
convert grams into vloume with the density of water being at
.997514 g/cm^3 at 23.1 Celsuis...
asked 6 hours ago -
Foreman company obtained a $20,000, 6% loan on May 1, 2018.
Principal and interest will be...
asked 6 hours ago -
5. Problem 11.05 (Discounted Payback)
eBook
Project L costs $60,000, its expected cash inflows are $14,000
per...
asked 6 hours ago -
1. Which of the following is true about politics and health
organizations?
A. Health organizations are...
asked 7 hours ago -
A space vehicle is coasting at a constant velocity of 18.1 m/s
in the +y direction...
asked 8 hours ago -
5) Use the following balanced equation to answer questions
(a)-(i).
3 Cu(s) + 8 HNO3(aq) →...
asked 7 hours ago -
A three-year maturity bond with a 12% annual coupon rate is
currently traded at par $1000...
asked 8 hours ago