Theorem 14 and example 53 show that the IQ system matrix is symmetric positive definite (SPD)....

 

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Theorem 14 and example 53 show that the IQ system matrix is symmetric positive definite (SPD). However, a theoretically SPD matrix may cease to be numerically SPD if it has a large condition number. A Cholesky factorization (chapter3) can be used to factorize a SPD matrix using only half of the flops required by LU factorization but will fail due to attempting the square root of a negative number if the matrix ceases to be numerically SPD.Repeat example 54and use a Cholesky factorization without MDI regularization to solve the linear system. At what condition number does the Cholesky factorization fail? The following code fragment may be useful: from scipy. linalg import cholesky, cho_solve, LinAlgError try: L = cholesky (B, lower=True) except LinAlgError: print('Cholesky fails...') cho_solve ((L, True), f) else: a = Theorem 14 and example 53 show that the IQ system matrix is symmetric positive definite (SPD). However, a theoretically SPD matrix may cease to be numerically SPD if it has a large condition number. A Cholesky factorization (chapter3) can be used to factorize a SPD matrix using only half of the flops required by LU factorization but will fail due to attempting the square root of a negative number if the matrix ceases to be numerically SPD.Repeat example 54and use a Cholesky factorization without MDI regularization to solve the linear system. At what condition number does the Cholesky factorization fail? The following code fragment may be useful: from scipy. linalg import cholesky, cho_solve, LinAlgError try: L = cholesky (B, lower=True) except LinAlgError: print('Cholesky fails...') cho_solve ((L, True), f) else: a =