Thermal characterization of materials using Karhunen–Loève decomposition techniques – Part I. Orthotropic materials

References

• Mendioroz, A, Fuente-Dascal, R, Apiñaniz, E, and Salazar, A, 2009. Thermal diffusivity measurements of thin plates and filaments using lock-in thermography, Rev. Sci. Instrum. 80 (2009), pp. 0749004-1–0749004-9.
   Web of Science ®Google Scholar
• Batsale, JC, Battaglia, JL, and Fudym, O, 2004. Autoregressive algorithms and spatially random flash excitation for 2D non destructive evaluation with infrared cameras, Quant. InfraRed Thermogr. 1 (2004), pp. 5–20.
   Google Scholar
• Pradere, C, Hany, C, Toutain, J, and Batsale, JC, 2010. Thermal analysis for velocity, kinetics and enthalpy reaction measurements in microfluidic devices, Experiment. Heat Transf. 23 (2010), pp. 44–62.
   Web of Science ®Google Scholar
• Pearson, K, 1901. On lines planes of closes fit to system of points in space, London, Edinb., Dublin Philos. Mag. J. Sci. 2 (1901), pp. 559–572.
   Google Scholar
• Hotteling, H, 1933. Analysis of complex statistical variables into principal components, J. Educ. Psychol. 24 (1933), pp. 417–441.
   Google Scholar
• Karhunen, K, 1946. Uber lineare methoden füer wahrscheiniogkeitsrechnung, Ann. Acad. Sci. Fenn., Ser. A1, Math. Phys. 37 (1946), pp. 3–79.
   Google Scholar
• Loève, MM, , Probability Theory, Van Nostrand, Princeton, NJ, 1988.
   Google Scholar
• Deprettere, F, , SVD and Signal Processing: Algorithms, Analysis and Applications, Elsevier Science, Amsterdam, 1988.
   Google Scholar
• Everitt, BS, and Dunn, G, 2001. Applied Multivariate Data Analysis. London: Arnold; 2001.
   Google Scholar
• Everit, BS, Landau, S, and Leese, M, 2001. Cluster Analysis. London: Arnold; 2001.
   Google Scholar
• Berry, MW, Dumais, ST, and Obrien, GW, 1995. Using linear algebra for intelligent information-retrieval, SIAM Rev. 37 (1995), pp. 573–595.
   Web of Science ®Google Scholar
• Berkoz, G, Holmes, P, and Lumley, JL, 1993. The proper orthogonal decomposition in the analysis of turbulent flows, Annu. Rev. Fluids Mech. 25 (1993), pp. 539–575.
   Web of Science ®Google Scholar
• Holmes, P, Lumley, J, and Berkoz, G, 1996. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge: Cambridge Monographs on Mechanics, Cambridge University Press; 1996.
   Google Scholar
• Ait-Yahia, A, and Palomo del Barrio, E, 1999. Thermal systems modelling via singular value decomposition: direct and modular approach, Appl. Math. Model. 23 (1999), pp. 447–468.
   Web of Science ®Google Scholar
• Ait-Yahia, A, and Palomo del Barrio, E, 2000. Numerical simplification method for state-space models of thermal systems, Numer. Heat Transf. Part B 37 (2000), pp. 201–225.
   Web of Science ®Google Scholar
• Palomo del Barrio, E, 2003. An efficient computational method for solving large-scale sensitivity problems, Numer. Heat Transf. Part B 43 (2003), pp. 353–372.
   Web of Science ®Google Scholar
• Dauvergne, JL, and Palomo del Barrio, E, 2009. A spectral method for low-dimensional description of melting/solidification within shape-stabilized phase change materials, Numer. Heat Transf. Part B 56 (2009), pp. 142–166.
   Web of Science ®Google Scholar
• Dauvergne, JL, and Palomo del Barrio, E, 2010. Toward a simulation-free P.O.D. approach for low-dimensional description of phase change problems, Int. J. Thermal Sci. 49 (2010), pp. 1369–1382.
   Web of Science ®Google Scholar
• Park, HM, and Jung, WS, 1999. On the solution of inverse heat transfer using the Karhunen-Loève Galerkin method, Int. J. Heat Mass Transf. 42 (1999), pp. 127–142.
   Web of Science ®Google Scholar
• Park, HM, and Jung, WS, 2001. The Karhunen–Loève Galerkin method for the inverse natural convection problems, Int. J. Heat Mass Transf. 44 (2001), pp. 155–167.
   Web of Science ®Google Scholar
• Palomo del Barrio, E, 2003. Multidimensional inverse heat conduction problems solution via Lagrange theory and model size reduction techniques, Inverse Probl. Engrg. 11 (2003), pp. 515–539.
   Web of Science ®Google Scholar
• Jolliffe, IT, 1986. Principal Components Analysis. New York: Springer; 1986.
   Google Scholar
• Golub, G, and Van Loan, C, 1996. Matrix Computation. Baltimore, MD: Johns Hopkins University Press; 1996.
   Google Scholar
• Strang, G, 1998. Introduction to Linear Algebra. Wellesley: Wellesley Cambridge Press; 1998.
   Google Scholar
• Berry, MW, 1992. Large-scale sparse singular value computation, Int. J. Supercomputer Appl. 6 (1992), pp. 13–49.
   Web of Science ®Google Scholar
• Jessup, ER, and Sorensen, DC, 1994. A parallel algorithm for computing singular-value decomposition of a matrix, SIAM J Matrix Anal. Appl. 15 (1994), pp. 530–548.
   Web of Science ®Google Scholar
• Intissar, A, 1997. Analyse Fonctionnelle et Théorie Spectrale Pour les Opérateurs Compacts Non Autoadjoints. Toulouse: Cépaduès-Éditions; 1997.
   Google Scholar
• Fan, K, and Hoffman, J, 1955. Some metric inequalities if the space of matrices, Proc. Amer. Math. Soc. 6 (1955), pp. 111–116.
   Google Scholar
• Mirsky, L, 1960. Symmetric gauge functions and unitarily invariant norms, Quart. J. Math. Oxford 11 (1960), pp. 50–59.
   Google Scholar
• Wellele, O, and Barrio, EPalomo del, , Experimental device for phase change analysis at the pore scale, Tech. Rep., Development of materials for thermal energy storage at high temperature, TREFLE Laboratory, University of Bordeaux, Bordeaux, 2008.
   Google Scholar