11.2 Find the norm low() for the nat member of an Orthogonal Set 6,(1) = x...
(a) Check that {1, 2} is an orthogonal set with the weight function w(x) = x2 on the interval (-2,2). (b) Find a quadratic polynomial p(x) = 32 + ax + b that is orthogonal to the functions in the set, with the same weighted inner product. (c) Is this set complete, as an orthogonal set with the weighted inner product?
using the orthogonal Find the Fourier-Bessel series on (0, R] of the function f(x) set Ja (Az2x) (に1, 2, . . . ). using the orthogonal Find the Fourier-Bessel series on (0, R] of the function f(x) set Ja (Az2x) (に1, 2, . . . ).
Problem 1. Let the inner product (,) be defined by (u.v)xu (x)v (x) dx, and let the norm Iilbe defined by lIul-)Corhe target funtio), and work with the approximating space P4 Use Gram-Schmidt orthogonalization with this inner product to find orthogonal polynomials (x) through degree four. Standardize your polynomials such that p: (1) 1. (a) Form the five-by-five Gram matrix for this inner product with the basis functions p (x) degree 4 approximation o f (x) using the specified norm,...
Problem 1. Let the inner prodct )be deined by (u.v)xu (x) v (x) dx, and let the norm |I-ll be defined by ull , ).Consider the target function f (x) with the approximating space P e', and work 2. Use Gram-Schmidt orthogonalization with this inner product to find orthogonal polynomials p (x) through degree four. Standardize your polynomials such that p, (1) 1 (b) Find the best degree 4 approximation to f(x) using the specified norm, and working with this...
using the orthogonal Find the Fourier-Bessel series on (0, R] of the function f(x) set Ja (Az2x) (に1, 2, . . . ).
Problem # 8: Consider the functions fl (x)-x and f2(x)-6-10cx on the interval [0, 1] a) Find the value of the constant c so that fı and f2 are orthogonal on [0, 1]. (b) Using the value of the constant c from part (a), find the norm of f2 on the interval [0,1 Enter your answer symbolically, as in these examples Problem #8(a): Problem #8(b):
Find the value of the linear correlation coefficient r. x 22.1 11.2 y 6 10 11.8 20.5 35.4 5 7 10 O A. 0.329 OB. O O c. 0.370 OD. -0.37
(a) Find the orthogonal projection Pf(x) of a) i/2 onto the subspace of Question 1 (b) Express P in the form of an integral operator Pf(x)K(x,y)f(y) dy and find the kernel K(x, y)
0 6. 11 points HoltLinAlg2 10.2.012. My Notes Ask Your Teacher Find projsf for Rx)- ex, where S-span1, x and the inner product is eBook 7. 1 points HoltLinAlg2 10.2.014 My Notes Ask Your Teacher Use the Gram-Schmidt process to convert the given set of vectors to an orthogonal basis with respect to the given inner product. (Apply the Gram-Schmidt process in the order the vectors are given and do not normalize.) The set,1,0with respect to the inner product (u,...
partial differential equations question Problem 6. a) Find all possible surfaces orthogonal to the planes x + 2y + cz = 1, where c is an arbitrary real constant. (b) Find the surface orthogonal to the planes x+2y+cz = 1 passing through the curve I: x = s, y = s, z = sa.