सरलतम रूप में एक ऐसा अंतर्वेशन बहुपद प्राप्त कीजिए जो निम्नलिखित आंकड़ों को आसंजित करता हो :
| x | -1 | 0 | 1 | 2 |
| f (x) | 3 | -4 | 5 | -6 |
दिए गए बिंदु हैं ((-1,3), (0,-4), (1,5), (2,-6))। चार बिंदुओं के लिए सरलतम अंतर्वेशन बहुपद _______ ___ _______ _________ ______ ___.
__________ _______ ___ __________ ______ ____ _________ ________ ___ ______ ____.
_____ ___ ________ _____ _________ ___ ____ ____ ________ _________ ______.
________ ______ _________ _______ __________ ____ _______ ______ __________ _____.
___ ________ ____ ___ __________ ____.
_____ __________ ________ __________ _____ ________ ______ _______ _________ ___ _________.
___ ___ _________ _________ _________ ________ _________ ______.
________ __________ ______ ______ ________.
______ ________ _______ _______ _______ _________ ___.
_________ ____ _____ _____ ____.
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List two distinct cosets of in D10, where r is a reflection in D10.
Determine the largest eigenvalue in magnitude and the corresponding eigenvector of the matrix using the power method. Take (1, 0, 0)T as the initial approximation and perform 4 iterations.
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।
Find the approximate root of the equation using Newton-Raphson method. Perform only 3 iterations with
.
Divide the polynomial
x5 - 6x4 + 8x3 + 8x2 + 4x - 40
by (x - 3) by the synthetic division method and find the remainder.
Set up the Gauss-Seidel iteration scheme in matrix form for solving the system of equations
Show that the method is convergent and hence find its rate of convergence.
) Evaluate by using trapezoidal rule with
and
. Use Romber's method to find the best value of
.
) Estimate the eigenvalues of the matrix
using the Gerschgorin bounds.