References
- Pearson, K, 1901. On lines planes of closes fit to system of points in space, Lond. Edinb. Dublin Philos. Mag. J. Sci. 2 (1901), pp. 559–572.
- Karhunen, K, 1946. Ueber lineare Methoden der Wahrscheinigkeitsrechnung, Ann. Acad. Sci. Fennicae A1 Math. Phys. 37 (1946), pp. 3–79.
- Loeve, MM, 1955. Probability Theory. Princeton, NJ: Van Nostrand; 1955.
- Hotelling, H, 1983. Analysis of complex of statistical variables into principal components, J. Educ. Psychol. 24 (1983), pp. 417–441.
- Sirovich, L, 1995. "Empirical eigenfunctions and low dimensional systems". In: Sirovich, L, ed. New Perspective in Turbulence. Berlin: Springer-Verlag; 1995.
- Feeney, BF, and Kappangantu, RJ, 1998. On the physical interpretation of proper orthogonal modes in vibrations, J. Sound Vib. 211 (1998), pp. 607–616.
- Wu, CG, Liang, YC, Lin, WZ, Lee, HP, and Lim, SP, 2003. A note on equivalence of proper. orthogonal decomposition methods, J. Sound Vib. 265 (2003), pp. 1103–1110.
- Press, WH, Teukolsky, SA, Vetterling, WT, and Flannery, BP, 1992. Numerical Recipes in FORTRAN 77. New York: Cambridge University Press; 1992.
- V. Buljak and G. Maier, Proper Orthogonal Decomposition and Radial Basis Functions in material characterization based on instrumented indentation, Eng. Struct. 33 (2011), pp. 492–501.
- G. Bolzon and V. Buljak, An effective computational tool for parametric studies and identification problems in materials mechanics, Comput. Mech. 48 (2011), pp. 675–687.
- V. Buljak and G. Maier, Identification of residual stresses by instrumented elliptical indentation and inverse analysis, Mech. Res. Comm. 41 (2012) pp. 21–29.
- Tikhonov, AN, and Arsenin, VA, 1994. Solution of Ill-posed Problems. New York: Wiley & Sons; 1994.
- Alifanov, OM, 1994. Inverse Heat Transfer Problems. Berlin: Springer-Verlag; 1994.
- Beck, JV, Blackwell, B, and St. Clair, CR, 1985. Inverse Heat Conduction: Ill-posed Problems. New York: Wiley & Sons; 1985.
- Ozisik, MN, and Orlande, HRB, 2000. Inverse Heat Transfer: Fundamentals and Applications. New York: Taylor & Francis; 2000.
- Bialecki, RA, Kassab, AJ, and Fic, A, 2004. Proper orthogonal decomposition and modal analysis for acceleration of transient fem thermal analysis, Int. J. Numer. Methods Eng. 62 (2004), pp. 774–797.
- Fic, A, Bialecki, RA, and Kassab, AJ, 2005. Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite-element. method, Numer. Heat Transfer 48 (2005), pp. 103–124.
- Ostrowski, Z, Bialecki, RA, and Kassab, AJ, 2005. Estimation of constant thermal conductivity by use of proper orthogonal decomposition, Comput. Mech. 37 (2005), pp. 52–59.
- Ostrowski, Z, Białecki, RA, and Kassab, AJ, 2008. Solving inverse heat conduction problems using trained POD-RBF network inverse method, Inverse Probl. Sci. Eng. 16 (1) (2008), pp. 39–54.
- Klimanek, A, , Numerical modeling of heat, mass and momentum transfer in natural draft wet cooling tower, Ph.D. thesis, Silesian University of Technology, Gliwice, Poland, 2010.
- Rogers, C, , Parameter estimation in heat transfer and elasticity using trained POD-RBF network inverse methods, M.Sc. thesis, University of Central Florida, Orlando, FL, 2010.
- Ostrowski, Z, Klimanek, A, and Bialecki, RA, 2010. CFD two-scale model of a wet, natural draft cooling tower. Numer. Heat Transfer 57 (2010), pp. 119–137.
- Sanford, RJ, 2003. Principles of Fracture Mechanics. Upper Saddle River, NJ: Pearson Education; 2003.
- Anderson, TL, 2005. Fracture Mechanics: Fundamentals and Applications. Boca Raton, FL: CRC Press; 2005.
- Hardy, RL, 1971. Multiquadric equations of topolography and other irregular surfaces, J. Geophys. Res. 76 (1971), pp. 1905–1915.
- Hardy, RL, 1990. Theory and applications of the multiquadricbiharmonic. method: 20 years of discovery 1968–1988, Comput. Math. Appl. 19 (8–9) (1990), pp. 163–208.
- Cheng, AH-D, Golberg, MA, Kansa, EJ, and Zammito, G, 2003. Exponential. convergence and H-c multiquadric collocation method for partial differential equations, Numer. Methods P.D.E. 19 (5) (2003), pp. 571–594.
- Divo, EA, and Kassab, AJ, 2007. An efficient localized RBF meshless method for fluid flow and conjugate heat transfer, ASME J. Heat Transfer 129 (2007), pp. 124–136.
- Divo, E, and Kassab, AJ, 2008. Localized meshless modeling of natural convective viscous flows, Numer. Heat Transfer, Part B: Fundam. 53 (2008), pp. 487–509.
- Divo, E, Kassab, AJ, Kapat, JS, and Chyu, MK, 1999. Retrieval of Multidimensional Heat Transfer Coefficient Distributions Using an Inverse BEM-based. Regularized Algorithm: Numerical and Experimental Results, ASME Paper HTD, Vol.; 1999, 364-1, ASME Press, New York, pp. 235–244.
- Kassab, AJ, Divo, E, Kapat, JS, and Chyu, MK, 2005. Retrieval of multi-dimensional heat transfer coefficient distributions using an inverse BEM-based regularized algorithm: Numerical and experimental examples, Eng. Anal. 29(2) (2005), pp. 150–160.
- Hansen, PC, and O'Leary, DP, 1993. The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput. 14 (1993), pp. 1487–1503.
- Hansen, PC, Jensen, TK, and Rodriguez, G, 2007. An adaptive pruning algorithm for the discrete L-curve criterion, J. Comput. Appl. Math. 198 (2007), pp. 483–492.
- Wirgin, A, , The Inverse Crime; available at http://arxiv.org/pdf/math-ph/0401050v1.pdf.