Jacobi's method for a symmetric matrix A is described by A] = A, A2 = P\A\P{ and, in

Chapter 9, Problem 15

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Jacobi's method for a symmetric matrix A is described by A] = A, A2 = P\A\P{ and, in general. A,+| = P,A,P/.The matrix Ai+\ tends to a diagonal matrix, where P, is a rotation matrix chosen to eliminate a large off-diagonal element in A,. Suppose cij^ and a^j are to be set to 0, where j ^ k.\iajj ^ a^k, then (Pi)jj = (Pi)kk = t/^ ( 1 + where or, if ajj = aklc. 2 V Vc2 + b 2 J' (Pi)kj / ^ ^ ~(Pi)jk, 2(Pi)jjv c + b 2 c - 2a]ksgn(ajj - akk) and b - \ajj - akk\ \J2 (Pi)jJ = (Pi)kk = and sfl (P,)kj = -(P,).ik = . Develop an algorithm to implement Jacobi's method by setting aai = 0. Then set a^, a^, 4i, an, ^43,... , an i,... , a,n_i in turn to zero.This is repeated until a matrix Ak is computed with n n 'j ,=1 7=1 jyti