(3) (a) Given a set of discrete pairs of data points {(xi, f) i = 0,1,2,...,nl,...
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following interpolating polynomials, and use MATLAB to graph both the interpolating polynomials and the data points: a) The piecewise linear Lagrange interpolating polynomialx) b) The piecewise quadratic Lagrange interpolating polynomial q(x) c) Newton's divided difference interpolation pa(x) of degree s 4
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following...
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i
+ 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1,
f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the
data point (0, 3), find a Newton form for the Lagrange polynomial
interpolating all 5 data points.
3. (25 pts) Let (r,, f()), 0,3, be data...
Need help, will rate, thanks.
3. Given n 1 data pairs (xo, yo), (xi,yi),..., (^n, Jn), define for j 0, 1,...,n the functions pj - Ilifj (zj-zi), and let also ψ(x)-111-o(x-xi) (a) Show that pj-(xj) (b) Show that the interpolating polynomial of degree at most n is given by yj
MATH 220 Project 1 Polynomial Curve Fitting It desired to fit a polynomial curve through evenly spaced (x-direction) points. The general form of a polynomial is: f(x) = 4,x" +47-1X2-1 + + ax + ao If one wishes to fit a curve through, say 4 points, one would need a 3rd degree polynomial (n = 3) such that 4 unknown constants could be evaluated. In the absence of availability of many wathematical programming tools (Matlab, etc., Mathematica is available as...
Given the data points (xi , yi), with
xi 0 1.2 2.3 3.5 4
yi 3.5 1.3 -0.7 0.5 2.7
find and plot (using MATLAB) the least-squares basis functions
and the resulting least-squares fitting functions together with the
given data points for the case of
a) a linear monomial basis p(x)= {1 x}T .
b) a quadratic monomial basis p(x)= {1 x
x2}T .
c) a trigonometric basis p(x)= {1 cosx sinx}T
Moreover, determine the coefficients a by the Moore-Penrose...
Linear Algebra. please complete or show me how to to
complete it. idk what to do. thank you
Curve Fitting It is desired to fit a polynomial curve through evenly spaced (x-direction) points. The general form of a polynomial is: f(x) = 4x + 4-1x* +ajx + ao If one wishes to fit a curve through, say 4 points, one would need a 3rd degree polynomial (n = 3) such that 4 unknown constants could be evaluated. In the absence...
A wind tunnel test conducted on an airfoil section yielded the following data between the lift coefficient (CL) and the angle of attack (?): 12 1.40 16 1.71 20 1.38 de CL 0.11 0.55 0.95 You are required to develop a suitable polynomial relationship between ? and CL and fit a curve to the data points by the least-squares method using (a) hand calculations and (b) Matlab programming Hint: A quadratic equation (parabola) y(x)-aa,x +a x' can be used in...
Consider the following table of data points:
Using least squares fitting, find the polynomial Q(x) of degree
2 that fits the data points given in the table above. Approximate
f(0.3) using Q(0.3).
Use P(x) = Ax2+Bx +C to find 3 equations and then
find A,B,C.
f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663 6 0.750 0.56978 0.875 0.46504 8 1.000 0.36788
Consider the following data table: 0 2i = 0.2 0.4 f(xi) = 2 2.018 2.104 2.306 0.6 0.2 and 23=0.4 is The linear Lagrange interpolator L1,1 (2) used to linearly interpolate between data points 12 (Chop after 2 decimal places) None of the above. -2.50x+0.20 -5.00x+2.00 -5.00x+2.00 5.00x-1.00 Consider the following data table: 2 Ti = 0 0.2 0.4 0.6 f(x) = 2.018 2.104 2.306 0.2 and 23 = 0.4, the value obtained at 2=0.3 is Using Lagrange linear interpolation...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...