Question

8 The zeroeth divided difference of the function f, with respect to
x i
, denoted by
f[x i ]
is the same as



f[x i ]=f(x i )



f[x 0 ]=f(x i )



f[x]=f(x i )



f[x]=f(xi)





9 The quantity
L 0 (x)
of the Lagrange’s interpolating polynomial P(x) is equal to



(x−x 1 )(x−x 2 )(x−x 3 )(x 0 −x 1 )(x 0 −x 2 )(x 0 −x 3 )



(x−x 1 )(x1−x 2 )(x 0 −x 3 )(x 0 −x 1 )(x 0 −x 2 )(x 0 −x 3 )



(x−x 1 )(x−x 2 )(x−x 3 )(x−x 1 )(x−x 2 )(x−x 3 )



(x−x 1 )(x−x 0 )(x−x 3 )(x 0 −x 4 )(x 0 −x 2 )(x 0 −x 3 )





10 A square matrix is called ………….. if all the elements above the main diagonal vanish.

upper triangular
triangular

lower triangular

rectangular

Answer 1

Answer on Question #55523 - Math – Algorithms | Quantitative Methods

1. The zeroeth divided difference of the function $f$, with respect to $x_i$, denoted by $f[x_i]$ is the same as

a) $f[x_i] = f(x_i)$

b) $f[x_0] = f(x_i)$

c) $f[x] = f(x_i)$

d) $f[x] = f(x_i)$

2. The quantity $L_0(x)$ of the Lagrange's interpolating polynomial $P(x)$ is equal to

a) $\frac{(x - x_1)(x - x_2)(x - x_3)}{(x_0 - x_1)(x_0 - x_2)(x_0 - x_3)}$

b) $\frac{(x - x_1)(x_1 - x_2)(x_0 - x_3)}{(x_0 - x_1)(x_0 - x_2)(x_0 - x_3)}$

c) $\frac{(x - x_1)(x - x_2)(x - x_3)}{(x - x_1)(x - x_2)(x - x_3)}$

d) $\frac{(x - x_1)(x - x_0)(x - x_3)}{(x_0 - x_4)(x_0 - x_2)(x_0 - x_3)}$

3. A square matrix is called ... if all the elements above the main diagonal vanish.

a) upper triangular

b) triangular

c) lower triangular

d) rectangular

Answer:

1. a)

2. a)

3. c)

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