3. Use Neville's method to obtain the approximations for Lagrange interpolating polynomials of degree one, two, and three to approximate each of the following: (a) f(8.4) if f(8.1) = 16.94410, f(8.3) = 17.56492, f(8.6) = 18.50515, f(8.7) = 18.82091 (b) f() if f(-0.75) = -0.07181250, f(-0.5) = -0.02475000, f(-0.25) = 0.33493750, f(0) = 1.10100000 (c) f(0.25) if f(0.1) = 0.62049958, f(0.2) = -0.28398668, f(0.3) = 0.00660095, f(0.4) = 0.24842440 (d) f(0.9) if f(0.6) = -0.17694460, f(0.7) = 0.01375227, f(0.8) = 0.22363362, f(1.0) = 0.65809197
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- The following is used to model a wave that impacts a concrete wall created by the US Navy speed boat.1. Derive the complete piecewise function of F(t) and F()The concrete wall is 2.8 m long with a cross-section area of 0.05 m2. The force at time equal zero is 200 N. It is also known that the mass is modeled as lumped at the end of 1200 kg and Young’s modulus of 3.6 GPa2. Use *Matlab to simulate and plot the total response of the system at zero initial conditions and t0 = 0.5 susing the R applicationConsider a gas in a piston-cylinder device in which the temperature is held constant. As the volume of the device was changed, the pressure was mecas- ured. The volume and pressure values are reported in the following table: Volume, m Pressure, kPa, when I= 300 K 2494 1247 831 4 623 5 499 416 (a) Usc lincar interpolation to estimate the pressure when the volume is 3.8 m. (b) Usc cubic splinc interpolation to cstimate the pressure when the vol- ume is 3.8 m. (c) Usc lincar interpolation to cstimate the volume if the pressure is meas- ured to be 1000 kPa. (d) Usc cubic splinc interpolation to cstimate the volume if the pressure is mcasured to be 1000 kPa. 4.
- olve the following initial value problems for the systems of equations using the matrix method. Findeigenvalues and eigenvectors and fix the undetermined coefficients by using technology (for example,Matlab or WolframAlpha)(a)x′ = x + 2y + 2zy′ = 2x + 7y + zz′ = 2x + y + 7z, x(0) = 9, y(0) = 1, z(0) = −1.(b)x′ = 9x − 7y − 5zy′ = −12x + 7y + 11z + 9wz′ = 24x − 17y − 19z − 9ww′ = −18x + 13y + 17z + 9w, x(0) = 2, y(0) = 0, z(0) = 1, w(0) = 1Construct the system for a free cubic spline for the following data, and solve it using MATLABto construct the polynomials. Write out the linear system, and the final si(x) polynomials. x -0.5 -0.25 0 f(x) -0.0247500 0.3349375 .101000011. Assume that a function f is in polynomial time and can be computed in time 0(n) and that g is in polynomial time and can be computed in time 0(n°). Prove that f composed with g, that is f(g(x)), can be computed in time 0(n5).
- using equation method for Hamming code of (7,4),determine of the Following messages m1 = 1111 & %3D m2=1010 (solution by Hamming codes)Consider the system of linear equations X2 + 2x3 X4 -1 X1 X2 X3 -X1 X2 + X3 + 3.x4 1 - Xị + 2x2 X4 9 Use Matlab to find the LU decomposition of the coefficient matrix A and then solve the resulting triangular system using forward and backward substitutions programs. (You need to provide the codes)ignore " Then use Theorem 3.3 in theBurden & Faires textbook to find an error bound for the approximations you obtained but do the rest please with the proper steps and please do not use chat gpt! Thank you !
- Using the three-variable Karnaugh-map below Solve for its corresponding function expression Replot the function from part (1) on a different three-variable Karnaugh-map (Hint: try a different combination of variables)Apply the Newton-Raphson method to approximate the root of the nonlinear equation x^4 - x - 10 = 0 Compute and presets the results of five iterates for each of the initial guesses x0=1, x0=2, x0=100. What are the observations?