Graphing using a Lagrange Interpolating Polynomial and Piecewise Linear Function

1. For medical purposes the level of sugar was measured in blood (in mg/dl). The samples were taken with 1 2hr increments, as the following table shows: initial sample 96 mg/dl after 30 min. 133 mg/dl after 60 min. 142 mg/dl after 90 min. 81 mg/dl after 120 min. 87 mg/dl Graph in MATLAB sugar curves corresponding to thes ...continues

Legrende Polynomials, Gaussian Quadrature and Rodrigues Formula

Please see the attached file for the fully formatted problems.

Suppose that N(h) is an approximation to M for every h > 0 and...

(See attached file for full problem description with proper equations and exponents) --- 1. Suppose that N(h) is an approximation to M for every h > 0 and that M = N(h)+K1h2+K2h4+K3h6+….. For some value K1, K2, K3… Use the values N(h), N(h/3), and N(h/9) to produce an O(h6) approximation to M. ---

Approximate the integrals using the Trapezoidal rule and Simpson's rule.

1. Approximate the integrals using the Trapezoidal rule. a) Integral from -0.5 to 0 x ln(x+1) dx b) Integral from 0.75 to 1.3 ((sin x)2 - 2x sin x +1) dx 2. Find a bound for error in question 1. using the error formula, and compare this to the actual error. 3. Repeat question 1. using Simpson's rule 4. Repeat ques ...continues

Trapezoid and Simpson's : The trapezoid rule applied to the integral from 0 to 2 f(x) dx gives the value 5, and the midpoint rule gives the value 4. What value does Simpson's rule give?

The trapezoid rule applied to the integral from 0 to 2 f(x) dx gives the value 5, and the midpoint rule gives the value 4. What value does Simpson's rule give?

Fixed Point Iteration Problem Using Matlab

Given the function f(x) =1 + 0.5 sin x, show that it has a unique fixed point x* in the interval I=[0,2] and that the iterations xn+1=f(xn) converge to the fixed point for any x0 Є I. Also, find the number of iterations necessary to guarantee that |xn - x* | < 10^-2 . Write a short Matlab code to find the fixed po ...continues

Proving an Inequality : Let an, n>= 1 be an increasing sequence of positive real numbers. Prove that 1/a1 + 2/(a1 + a2) + .... + n/(a1 +... + an) < 4(1/a1 + 1/a2 + ... + 1/an)

Let an, n>= 1 be an increasing sequence of positive real numbers. Prove that 1/a1 + 2/(a1 + a2) + .... + n/(a1 +... + an) < 4(1/a1 + 1/a2 + ... + 1/an) Can anything be said about the constant 4? ---

Proving an Equality : Lagrange Interpolating Polynomials

Let be distinct points and let . Show that for m = 1,2,…,n and for all x. Please see the attached file for the fully formatted problems.

Scatter Diagrams, Slope of Regression Equation and Coefficient of Correlation

Super Markets, Inc. is considering expanding into the Scottsdale, Arizona, area. Ms. Luann Miller, Director of Planning, must present an analysis of the proposed expansion to the operating committee of the board of directors. As a part of her proposal, she needs to include information on the amount people in the region spend per ...continues

Numerical Linear Algebra : Unitary and Triangular Matrices and Krylov Matrix

1. Let A = QR be the factorization of a A into the product of a unitary matrix and a trianglular matrix. Suppose that the cloumns of A are linearly independent. Show that |rkk| is the distance from the k-th column of A to the linear space spanned by the first k-1 columns of A. 2. Let A Є C^(mxm) and b Є C^m be abi ...continues