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“…The value of the objective function in the VMMAP cannot be decreased below 1.32 £ 10 2 2 , and continuing more iterations results in non-convergence. It might worth mentioning that the same behavior of the reduction function using BFGS version of VMM was also observed in Molavi et al (2010b) for one-dimensional problem. Furthermore, no convergence is yielded with or without errors in the simulated data when the developed technique by equation ( 14) is employed.…”

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“…The value of the objective function in the VMMAP cannot be decreased below 1.32 £ 10 2 2 , and continuing more iterations results in non-convergence. It might worth mentioning that the same behavior of the reduction function using BFGS version of VMM was also observed in Molavi et al (2010b) for one-dimensional problem. Furthermore, no convergence is yielded with or without errors in the simulated data when the developed technique by equation ( 14) is employed.…”

“…Their results indicated that the quasi-Newton method is faster and more accurate than the CGM in estimation of unknowns in the whole domain linear inverse problems. Recently Molavi et al (2010b) used a novel search gradient-type algorithm for the solution of one-dimensional linear Heat flux retrieval and non-linear IHCPs with and without moving boundary and compared their method to CGM and quasi-Newton methods. They showed that all studied algorithms could produce results with the same order of accuracy, while their method requires noticeably less number of iterations to converge.…”

“…(16) In CVDM, the variable z of a real function ,v(z) is replaced by a complex one z + 1h, with the imaginary part h very small (usually h= [10][11][12][13][14][15][16][17][18][19][20]. In the present work, it is used for the determination of the sensitivity coefficients matrix, which is composed of first order derivatives.…”

“…Heat transfer problems [1][2][3][4][5][6] and the corresponding numerical solution methods [7][8][9][10][11][12][13][14][15][16][17][18][19][20] have always been hot issues. In the heat transfer field, direct heat conduction problems are concerned with the determination of the temperature field when the domain, boundary and initial conditions, thermo-physical properties, and geometric conditions are specified.…”