Write the error in linear interpolation. Hence, show that
where
Consider two points ((x_0, f(x_0))) and ((x_1, f(x_1))). The linear interpolation (L(x)) between them is [ L(x) = f(x_0) + \frac{f(x_1) - f(x_0)}{x_1 - x_0}(x - x_0). ] The error in linear interpolation is [ E(x) = f(x) - L(x). ] _________ ________ ______ ___ _________ ___ ______ ___ ______ _____.
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Determine the order of convergence of the iterative method
for finding a simple root of the equation .
Find the approximate root of the equation using Newton-Raphson method. Perform only 3 iterations with
.
ऑयलर विधि से आदि मान समस्या को हल कीजिए$
लेते हुए y(3.1) ज्ञात कीजिए।
Evaluate by using trapezoidal rule with
and
. Use Romber's m
घात विधि द्वारा निम्नलिखित आव्यूह का परिमाण में अधिकतम आइगेनमान व संगत आइगेनसदिश ज्ञात कीजिए :$
प्रारम्भिक सन्निकटन (1, 0, 0)T लेकर 4 पुनरावृत्तियाँ कीजिए।
The Gauss-Seidel method is used to solve the system of equations
Determine the rate of convergence of the method.
State whether the following statements are true or false. Give a Short proof or a counter-example in support of your answer.
a) The equation has not root in the interval [3, 5].
b) , where E is the shift operator and
is the forward difference operator.
c) Every system of linear equations can be solved using the LU decomposition method.
d) For the data (2, 4), (1, 5), (3, 6) the Newton's divided difference f[x0, x1, x2] is .
e) The Newton-Raphson method cannot be used to find a cube root of a positive real number.