Q3: The Gauss-Seidel is considered to approximate the solution for the linear systemAž = b. Given0.5-0.250.5T.0.125-0.250.50 -0.0625 0.125 -0.25exact solution is i=[1 1 -1 1], with initial guess i) =0, and the secondapproximations is ) =[1.375 0.375 -0.46875 0.734375]. In l, norm, find1. the number of iterations necessary to achieve accuracy 10.2. the absolute error in approximating ï using *).3. the relative error in approximating ĩ using r).4. an error bound for approximating ï using i).

In the linear system Ax=B, the exact solution is x→=1 1 -1 1t The initial guass is x→(0)=0 0 0…

exact solution is i=[1 1 -1 1], with initial guess = Ö , and the second approximations is e) = [1.375 0.375 -0.46875 0.734375]. In l, norm, find 1. the number of iterations necessary to achieve accuracy 10. 2. the absolute error in approximating i using e). 3. the relative error in approximating i using . 4. an error bound for approximating i using ie).

exact solution is i=[1 1 -1 1], with initial guess = Ö , and the second approximations is e) = [1.375 0.375 -0.46875 0.734375]. In l, norm, find 1. the number of iterations necessary to achieve accuracy 10. 2. the absolute error in approximating i using e). 3. the relative error in approximating i using . 4. an error bound for approximating i using ie).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.

Question

Q3: The Gauss-Seidel is considered to approximate the solution for the linear system
Až = b. Given
0.5
-0.25
0.5
T.
0.125
-0.25
0.5
0 -0.0625 0.125 -0.25
exact solution is i=[1 1 -1 1], with initial guess i) =0, and the second
approximations is ) =[1.375 0.375 -0.46875 0.734375]. In l, norm, find
1. the number of iterations necessary to achieve accuracy 10.
2. the absolute error in approximating ï using *).
3. the relative error in approximating ĩ using r).
4. an error bound for approximating ï using i).

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