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Somnath posted an Question
August 29, 2020 • 15:03 pm 30 points
  • IIT JAM
  • Mathematics (MA)

4707ltoi 26. in general, the iteration method (x= ax,)) for computing the roots of an equation flx) = 0 is of linear convergence (order of convergence is 1). to

4707LTOI 26. In general, the iteration method (X= Ax,)) for computing the roots of an equation flx) = 0 is of linear convergence (order of convergence is 1). To increase the order of convergence, we select the iteration function dx)=x+ 4f(x)+2f (x)+, where 4's are arbitrary constants to be determined. Compute the 4 such that the order of convergence is quadratic (2); 4 and such that the order of convergence is cubic (3). Use these derived methods to compute the roots of the following equations correct to six decimal places a) 2x-cos(x) = 0 b)x+3sin(x) = 2e c)x+3x-5cos(x) =0 Ans. 0.450184 Ans. 0.355878 Ans. 0.895651

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