Let x1, x2, ... , xn be distinct points in the interval [-1, 1] and let where

Question:

Let x1, x2, ... , xn be distinct points in the interval [-1, 1] and let

where the Li's are the Lagrange functions for the points x1, x2, ... , xn.
(a) Explain why the quadrature formula

will yield the exact value of the integral whenever f(x) is a polynomial of degree less than n.
(b) Apply the quadrature formula to a degree 0 polynomial and show that
A1 + A2 + ...... + An =2

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:59 AM

See More Questions

Let X1, X2, . . . , Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X1. (b) S2 = X1 + X2. (c) Sn = X1 + X2 + + Xn. (d)...
Let x1, x2 be distinct points in a normed linear space X. There exists a continuous linear functional f X* that evaluates them differently, that is, such that f(x1) f(x2)
Let X1, X2, . . . , Xn be a random sample of Bernoulli trials b(1, p). (a) Show that a best critical region for testing H0: p = 0.9 against H1: p = 0.8 can be based on the statistic c) What is the...
1. If a firm has already paid an expense or is obligated to pay one in the future, regardless of whether a particular project is undertaken, that expense is a A. Committed cost B. Complementary cost...
A stockbroker advises a client to buy cumulative preferred stock. . . . With that type of stock, . . . [you] will never have to worry about losing the dividends. Is the broker right?
Draw the B.M. and S.F. diagrams for the beam loaded as shown in Fig. 15.37 . A 15kN/m B 3m Fig. 15.37 1.5m 150kN.m 1.5m D
How do you describe each of the models operations?
Instar Company has several investments in the securities of other companies. The following information regarding these investments is available at December 31, 2012. 1. Instar holds bonds issued by...
Jane Dutton, a co-founder of "Positive Organisational Scholarship" (POS), spoke to us. How did she describe POS in her talk? Refer to the video between 15:30 to 25:06 minutes:...
A plant supervisor must apportion her 40-hour workweek between hours working on the assembly line and hours supervising the work of others. She is paid $12 per hour for working and $15 per hour for...
Show that if f(x) is a polynomial of degree less than n then f(x) must equal the interpolating polynomial P(x) in (7), and hence the sum in (7) gives the exact value for ba f(x)w(x)dx.
Let x1, x2, ..., xn be the roots of the Legendre polynomial Pn. If the Ai's are defined as in Exercise 15, then the quadrature formula will be exact for all polynomials of degree less than 2n. (a) If...
Does grow faster, slower, or at the same rate as g as x? Give reasons for your answers. a. (x) = 3 -x , g(x) = 2 -x b. (x) = ln 2x, g(x) = ln x 2 c. (x) = 10x 3 + 2x 2 , g(x) = e x d. (x) = tan -1...
Ignoring the impact of any accounting change, the asset turnover ratio for Colorful Concepts excluding the investments in associates would: A. stay the same. B. increase by 0.10. C. decrease by 0.10....
Based on Gelblums estimates, if Zimt is deemed to have joint control of Oxbow, and Zimt uses the proportionate consolidation method, its 31 December 2010 total liabilities (in millions) will most...
Based on the ratios for operating cash flow before interest and taxes to operating income, Abay should conclude that: A. Bickchips earnings are backed by cash flow. B. Bickchips earnings are not...
Compared to Cinnamons operating margin in 2009, if it is deemed to have control of Cambridge, its operating margin in 2010 will most likely be: A. lower. B. higher. C. the same. Cinnamon, Inc. is a...
Based on Martinezs conclusions, Stellars financial statements are best categorized as: A. non-GAAP compliant. B. GAAP compliant, but with earnings management. C. GAAP compliant and decision useful,...
When a Cu-Zn alloy solidifies, one portion of the structure contains 25 at% zinc and another portion 0.025 mm away contains 20 at% zinc. The lattice parameter for the FCC alloy is about 3.63 x 10 -8...
For the following exercises, find the area of the triangle. Round to the nearest hundredth. 22 50 36
Find an equation for graph. -2 2 4
Find an equation for graph. 2 3 -2- 4)
Find an equation for graph.
If the nominal interest rate is 14%, and inflation is 4%, what is the real interest rate? 22.A bond investment yielded 8%. If inflation was 3%, what real return did the bond offer? 23.The following...
Bierce Corporation has two manufacturing departments--Machining and Finishing. The company used the following data at the beginning of the year to calculate predetermined overhead rates: Estimated...
Discuss how communication channels have changed over the years due to technology.

Let x1, x2, ... , xn be distinct points in the interval [-1, 1] and let where

Question:

.1 Ai= Li (x)dx, i=1 ,n f(x)dx = A1 f(xl ) + A2/(X2) + . . . + An f (x") -1

Step by Step Answer:

a The quadrature formula approximates the integral of fx by a sum which is equal to the exact v...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions