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ProblemsClear skill: Interpolation Approximation Build a practice set

ProblemCourse & topicStatus

NUM:9922151Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

—

NUM:9922152Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

—

NUM:9922153Derive the second-order central-difference formula for f''(x) by adding the Taylor expansions of f(x+h) and f(x-h)…

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

—

NUM:9922154Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922155Classify each of the following finite-difference operators as forward, backward, or central, and state the order…

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

—

NUM:9922156Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922157Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922158Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922159Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

—

NUM:9922160Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922161Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922162Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922163Derive the local (single-interval) trapezoidal rule…

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922164Apply Simpson's rule on a single pair of subintervals…

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922165Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922166Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922167Prove that Simpson's rule on two equal subintervals of width h is exact for every polynomial of degree at most 3.

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922168Classify each of the following Newton–Cotes formulae as open or closed, state the number of nodes, and state the…

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922169Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922170Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922171Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922172Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922173Prove that the n-point Gauss–Legendre quadrature rule on [-1,1] is exact for every polynomial of degree at most 2n-1.

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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NUM:9922174Mathematical problem title

Interpolation ApproximationNumerical Methods Problem Solving

Interpolation and approximationNumerical Methods · Calculation

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Showing 24 of 50 matching problems.

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Let

f(x)=e^{-x}\sin

x.

Let

f(x)=\ln(1+x^2)

.

The values f(1.0)=2.7183, f(1.1)=3.0042, f(1.2)=3.3201, and f(1.3)=3.6693 are given, where f is

C^4

on [1.0,1.3].

Let

D_h

f(x)=\bigl(f(x+h)-f(x-h)\bigr)/(2h)

be the central-difference approximation to f'(x).

The central-difference approximations

D_h(0.5)=0.852148

and

D_{h/2}(0.5)=0.846580

to f'(0.5) have been computed…

Let

N(h)

be a numerical approximation satisfying

N(h)=M+K_1 h^2+K_2 h^4+K_3 h^6+\cdots

.

Prove that if

N(h)=M+K h^p+O(h^q)

with

q>p>0

and

K\neq 0

, then the Richardson extrapolant…

The composite trapezoidal rule on

[a,b]

with

n

equal subintervals of width

h=(b-a)/n

is…

Let

f(x)=\cos

x.

The composite trapezoidal rule error formula is

E_T=-\frac{(b-a)h^2}{12}f''(\xi)

for some

\xi\in(a,b)

, provided…

Let

f(x)=x^4

.

The composite Simpson error on

[a,b]

with even

n

and

h=(b-a)/n

is

E_S=-\frac{(b-a)h^4}{180}f^{(4)}(\xi)

…

The closed Newton–Cotes formula of order

n=4

(Boole's rule) on

[x_0,x_4]

with

h=(x_4-x_0)/4

is…

An n-point interpolatory quadrature rule on [a,b] has the form

\sum_{i=1}^n

w_i

f(x_i)

with distinct nodes…

The two-point Gauss–Legendre rule on

[-1,1]

is…

The three-point Gauss–Legendre nodes and weights on

[-1,1]

are…

Let

I(f)=\displaystyle\int_{-1}^{1}f(x)\,dx

and let

G_2(f)

denote the two-point Gauss–Legendre approximation.