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Journal articles on the topic 'Rayleigh- Ritz Method (RRM)'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Monterrubio, L. E. "Free vibration of shallow shells using the Rayleigh—Ritz method and penalty parameters." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 10 (2009): 2263–72. http://dx.doi.org/10.1243/09544062jmes1442.

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In the present work, the Rayleigh—Ritz method (RRM) and the penalty function method (PFM) are used to solve vibration problems of shallow shells of rectangular planform with spherical, cylindrical, and hyperbolic paraboloidal geometries with classical boundary conditions. Problems with more complicated constraints can also be solved using the method presented in this work, which consists in developing the stiffness and mass matrices of a completely free shallow shell using the RRM and then all constraints of the shell are defined by the PFM through the use of either artificial stiffness or art

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2

K., C. Nwachukwu, Ezeh J.C., Ibearugbulem O.M., Anya U.C., Atulomah F.K, and Mathew C.C. "Flexural Stability Analysis of Doubly Symmetric Single Cell Thin -Walled Box Column Based On Rayleigh- Ritz Method [RRM]." International Journal of Recent Research in Thesis and Dissertation (IJRRTD) 5, no. 1 (2024): 79–90. https://doi.org/10.5281/zenodo.10893911.

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<strong>Abstract:</strong> This research work is aimed at determining the Flexural [F] critical buckling load,  for Doubly Symmetrical Single (DSS) cell Thin-Walled Columns [TWC] cross section  at different boundary conditions using  Rayleigh-Ritz Method (RRM) with Polynomial Shape Functions . It is the follow up of the works by Nwachukwu and others (2017) and Nwachukwu and others (2021a) where the governing equation for the Total Potential Energy Functional (TPEF) for a Thin- Walled Box Column (TWBC) applicable to RRM and peculiar TPEF for DSS cross – section were derived

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3

Han, Jie, Xianglin Gong, Chencheng Lian, et al. "An Analysis of Nonlinear Axisymmetric Structural Vibrations of Circular Plates with the Extended Rayleigh–Ritz Method." Mathematics 13, no. 8 (2025): 1356. https://doi.org/10.3390/math13081356.

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The nonlinear deformation and vibrations of elastic plates represent a fundamental problem in structural vibration analysis, frequently encountered in engineering applications and classical mathematical studies. In the field of studying the nonlinear phenomena of elastic plates, numerous methods and techniques have emerged to obtain approximate and exact solutions for nonlinear differential equations. A particularly powerful and flexible method, known as the extended Rayleigh–Ritz method (ERRM), has been proposed. In this approach, the temporal variable is introduced as an additional dimension

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4

Mohsen-Nia, Mohsen, Fateme Abadian, Naeime Abadian, Keivan Mosaiebi Dehkordi, Maryam Keivani, and Mohamadreza Abadyan. "Analysis of cantilever NEMS in centrifugal-fluidic systems." International Journal of Modern Physics B 30, no. 22 (2016): 1650148. http://dx.doi.org/10.1142/s0217979216501484.

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Electromechanical nanocantilevers are promising for using as sensors/detectors in centrifugal-fluidic systems. For this application, the presence of angular speed and electrolyte environment should be considered in the theoretical analysis. Herein, the pull-in instability of the nanocantilever incorporating the effects of angular velocity and liquid media is investigated using a size-dependent continuum theory. Using d’Alembert principle, the angular speed is transformed into an equivalent centrifugal force. The electrochemical and dispersion forces are incorporated considering the corrections

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5

Morachkovska, Iryna, Lidiya Kurpa, Anna Linnik, Galina Timchenko, and Tetyana Shmatko. "Dynamic analysis of functional gradient porous sigmoidal sandwich plates." Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines, no. 1 (December 21, 2023): 39–44. http://dx.doi.org/10.20998/2078-9130.2023.1.281191.

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Analysis of free vibrations of functionally graded (FG) porous sigmoid sandwich plates, is considered in this paper. The plate can have a complex geometric shape and various types of fastening. To solve the problem, we used the variational-structural method (RFM), which combines the theory of R-functions and variational method of Rayleigh-Ritz. The mathematical statement of the problem is carried out within the framework of the deformation theory of plates of the first order (FSDT). Plates are considered, the outer layers of which are made of functionally graded materials (FGM), and the core i

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6

Žitňan, Peter. "The Rayleigh-Ritz method still competitive." Journal of Computational and Applied Mathematics 54, no. 3 (1994): 297–306. http://dx.doi.org/10.1016/0377-0427(94)90252-6.

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7

O Osuntoki, Joseph. "Advanced Solutions to Boundary Value Problems: A Comparative Study of Rayleigh-Ritz and the Finite Element Method." Innovative Journal of Applied Science 01, no. 01 (2024): 01–07. http://dx.doi.org/10.70844/ijas.2024.1.5.

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This study investigates the solution of a boundary value problem using two numerical methods: The Rayleigh-Ritz method and the Finite Element Method (FEM). The aim is to compare the performance of these methods and assess the reliability of FEM as a generalization of the Rayleigh-Ritz approach for more complex problems. The Rayleigh-Ritz method and the linear element formulation of the finite element method were employed to solve the boundary value problem. A detailed comparison of the results obtained from both methods was performed. Graphical illustrations were used to present the solutions,

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8

Stubbins, Calvin. "Recurrence Relations in the Rayleigh-Ritz Method." Progress of Theoretical Physics Supplement 138 (2000): 750–52. http://dx.doi.org/10.1143/ptps.138.750.

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9

Kumar, Yajuvindra. "The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review." Journal of Vibration and Control 24, no. 7 (2017): 1205–27. http://dx.doi.org/10.1177/1077546317694724.

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The Rayleigh–Ritz method is a classical method that has been widely used to investigate dynamic, static and buckling behavior, i.e., the natural frequencies, mode shapes, moments, stresses, critical buckling loads of vibrating structures and to solve boundary value problems. Different developments in the method have taken place from time to time. This paper presents a comprehensive literature review on the application of the Rayleigh–Ritz method to analyze vibration, static and buckling characteristics of beams, shells and plates using different theories.

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10

Liu, Xiao Wan, and Bin Liang. "Effect of Ring Support Position and Geometrical Dimension on the Free Vibration of Ring-Stiffened Cylindrical Shells." Applied Mechanics and Materials 580-583 (July 2014): 2879–82. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.2879.

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Effect of ring support position and geometrical dimension on the free vibration of ring-stiffened cylindrical shells is studied in this paper. The study is carried out by using Sanders shell theory. Based on the Rayleigh-Ritz method, the shell eigenvalue governing equation is derived. The present analysis is validated by comparing results with those in the literature. The vibration characteristics are obtained investigating two different boundary conditions with simply supported-simply supported and clamped-free as the examples. Key Words: Ring-stiffened cylindrical shell; Free vibration; Rayl

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11

Amore, Paolo, and Francisco M. Fernández. "Rayleigh–Ritz variation method and connected-moments expansions." Physica Scripta 80, no. 5 (2009): 055002. http://dx.doi.org/10.1088/0031-8949/80/05/055002.

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12

Wang, C. M., L. Wang, and K. K. Ang. "Beam‐Buckling Analysis via Automated Rayleigh‐Ritz Method." Journal of Structural Engineering 120, no. 1 (1994): 200–211. http://dx.doi.org/10.1061/(asce)0733-9445(1994)120:1(200).

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13

Yserentant, Harry. "A Short Theory of the Rayleigh–Ritz Method." Computational Methods in Applied Mathematics 13, no. 4 (2013): 495–502. http://dx.doi.org/10.1515/cmam-2013-0013.

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Abstract. We present some new error estimates for the eigenvalues and eigenfunctions obtained by the Rayleigh–Ritz method, the common variational method to solve eigenproblems. The errors are bounded in terms of the error of the best approximation of the eigenfunction under consideration by functions in the ansatz space. In contrast to the classical theory, the approximation error of eigenfunctions other than the given one does not enter into these estimates. The estimates are based on a bound for the norm of a certain projection operator, e.g., in finite element methods for second order eigen

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14

Behera, Laxmi, and S. Chakraverty. "Static analysis of nanobeams using Rayleigh–Ritz method." Journal of Mechanics of Materials and Structures 12, no. 5 (2017): 603–16. http://dx.doi.org/10.2140/jomms.2017.12.603.

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15

Hagedorn, P. "The Rayleigh-Ritz Method With Quasi-Comparison Functions in Nonself-Adjoint Problems." Journal of Vibration and Acoustics 115, no. 3 (1993): 280–84. http://dx.doi.org/10.1115/1.2930346.

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In the determination of the first eigenmodes of continuous linear elastic systems the Rayleigh-Ritz method is often used. It is also very useful in the discretization of the elastic members of multibody systems undergoing large nonlinear motions. Recently the concept of quasi-comparison functions has been introduced for the Rayleigh-Ritz discretization in self-adjoint eigenvalue problems, where it may lead to a considerable improvement of the convergence when compared with other classes of admissible functions. In this paper it is shown with a simple example that a similar phenomenon also hold

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16

Nwachukwu, K., J. Ezeh, H. Ozioko, J. Eiroboyi, and D. Nwachukwu. "Formulation Of The Total Potential Energy Functional Relevant To The Stability Analysis Of A Doubly Symmetric Single (DSS) Cell Thin- Walled Box Column In Line With Raleigh- Ritz Method." American Journal of Computing and Engineering 4, no. 1 (2021): 57–82. http://dx.doi.org/10.47672/ajce.815.

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Purpose: This work is concerned with the formulation of peculiar Total Potential Energy Functional (TPEF) for a Doubly Symmetric Single (DSS) cell Thin -walled Box Column (TWBC). The formulated Energy Functional Equations support the stability analysis of a DSS cell thin-walled box (closed) column cross-section using Raleigh - Ritz Method (RRM) with polynomial shape functions. Methodology: This present formulation is based on the governing TPEF developed by Nwachukwu and others (2017). The polynomial shape functions (only the first two coordinate polynomial shape functions) for different

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17

Cyprian, Nwasuka Nnamdi. "Geothermal Analysis of Uturu- Nigeria." International Journal of Emerging Science and Engineering 13, no. 1 (2024): 1–5. https://doi.org/10.35940/ijese.d8168.13011224.

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This paper presents the geothermal analysis of Uturu-Nigeria using the Rayleigh-Ritz-Chebyshev collocation method. To develop the optimal geothermal design parameters for theUturu-okigwe axis, the developed model was used to analyze the geothermal performance and investigate the effects of geothermal parameters using a longitudinal fin. The results, however, showed that whenever there is an increase in convective, radioactive, and magnetic parameters, the rate of heat transferred from the geothermal longitudinal fin increases. The result also showed that the Rayleigh-Ritz-Chebyshev spectral co

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18

Nwasuka, Nnamdi Cyprian. "Geothermal Analysis of Uturu- Nigeria." International Journal of Emerging Science and Engineering (IJESE) 13, no. 1 (2024): 1–5. https://doi.org/10.35940/ijese.D8168.13011224.

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<strong>Abstract:</strong> This paper presents the geothermal analysis of Uturu- - Nigeria using the Rayleigh-Ritz-Chebyshev collocation method. To develop the optimal geothermal design parameters for the Uturu-okigwe axis, the developed model was used to analyze the geothermal performance and investigate the effects of geothermal parameters using a longitudinal fin. The results, however, showed that whenever there is an increase in convective, radioactive, and magnetic parameters, the rate of heat transferred from the geothermal longitudinal fin increases. The result also showed that the Rayl

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19

Elishakoff, Isaac, and Charles W. Bert. "Comparison of Rayleigh's noninteger-power method with Rayleigh-Ritz method." Computer Methods in Applied Mechanics and Engineering 67, no. 3 (1988): 297–309. http://dx.doi.org/10.1016/0045-7825(88)90050-3.

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20

Prado Leite, Leonardo Fellipe, and Fabio Carlos Da Rocha. "HIGH-ORDER ZIG-ZAG THEORIES TO STATIC LAMINATED COMPOSITE BEAM ANALYSIS BY THE RAYLEIGH-RITZ METHOD." Revista Sergipana de Matemática e Educação Matemática 9, no. 2 (2024): 48–62. http://dx.doi.org/10.34179/revisem.v9i2.19821.

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Technological advancements across various engineering fields have grown demand for highly efficient materials for specific applications. Laminated composite materials have emerged as a promising solution, offering a combination of favorable mechanical properties by layering different materials. Theories, such as zig-zag theories, have been developed to predict the mechanical behavior of these materials under external stresses. This study investigates the outcomes provided by the Rayleigh-Ritz variational method, employing different approximation functions, particularly focusing on unified high

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21

Dufour, R., and A. Berlioz. "Parametric Instability of a Beam Due to Axial Excitations and to Boundary Conditions." Journal of Vibration and Acoustics 120, no. 2 (1998): 461–67. http://dx.doi.org/10.1115/1.2893852.

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In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It is shown that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests en

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22

Bhattacharyya, Surashmi, and Arun Kumar Baruah. "On Rayleigh-Ritz Method in Three-Parameter Eigenvalue Problems." International Journal of Computer Applications 86, no. 3 (2014): 38–42. http://dx.doi.org/10.5120/14969-3149.

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23

Gopinathan, Senthil V., Vasundara V. Varadan, and Vijay K. Varadan. "Active noise control studies using the Rayleigh–Ritz method." Journal of the Acoustical Society of America 108, no. 5 (2000): 2477. http://dx.doi.org/10.1121/1.4743138.

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24

Pakiari, A. H., and F. M. Khalesifard. "Perturbation-variation Rayleigh-Ritz (PV-RR) method. Part I." Journal of Molecular Structure: THEOCHEM 417, no. 1-2 (1997): 169–74. http://dx.doi.org/10.1016/s0166-1280(97)00094-8.

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25

Chakraverty, S., and Laxmi Behera. "Free vibration of rectangular nanoplates using Rayleigh–Ritz method." Physica E: Low-dimensional Systems and Nanostructures 56 (February 2014): 357–63. http://dx.doi.org/10.1016/j.physe.2013.08.014.

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26

Liew, K. M., and C. M. Wang. "pb-2 Rayleigh - Ritz method for general plate analysis." Engineering Structures 15, no. 1 (1993): 55–60. http://dx.doi.org/10.1016/0141-0296(93)90017-x.

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27

Fernández, Francisco M. "Rayleigh-Ritz variation method and connected-moments polynomial approach." International Journal of Quantum Chemistry 109, no. 4 (2009): 717–19. http://dx.doi.org/10.1002/qua.21854.

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28

Guo, Wenjie, and Qingsong Feng. "Free Vibration Analysis of Arbitrary-Shaped Plates Based on the Improved Rayleigh–Ritz Method." Advances in Civil Engineering 2019 (October 17, 2019): 1–14. http://dx.doi.org/10.1155/2019/7041592.

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In this investigation, an improved Rayleigh–Ritz method is put forward to analyze the free vibration characteristics of arbitrary-shaped plates for the traditional Rayleigh–Ritz method which is difficult to solve. By expanding the domain of admissible functions out of the structural domain to form a rectangular domain, the admissible functions of arbitrary-shaped plates can be described conveniently by selecting the appropriate admissible functions. Adopting the spring model to simulate the general boundary conditions, the problems of vibration of the arbitrary plate domain can be solved perfe

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29

Fernández, Francisco M. "Variational approach to the Schrödinger equation with a delta-function potential." European Journal of Physics 43, no. 2 (2021): 025401. http://dx.doi.org/10.1088/1361-6404/ac3f27.

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Abstract We obtain accurate eigenvalues of the one-dimensional Schrödinger equation with a Hamiltonian of the form H g = H + gδ(x), where δ(x) is the Dirac delta function. We show that the well known Rayleigh–Ritz variational method is a suitable approach provided that the basis set takes into account the effect of the Dirac delta on the wavefunction. Present analysis may be suitable for an introductory course on quantum mechanics to illustrate the application of the Rayleigh–Ritz variational method to a problem where the boundary conditions play a relevant role and have to be introduced caref

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30

Morales, C. "Rayleigh-Ritz Based Substructure Synthesis for Multiply Supported Structures." Journal of Vibration and Acoustics 122, no. 1 (1998): 2–6. http://dx.doi.org/10.1115/1.568430.

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This paper is concerned with the convergence characteristics and application of the Rayleigh-Ritz based substructure synthesis method to structures for which the use of a kinematical procedure taking into account all the compatibility conditions, is not possible. It is demonstrated that the synthesis in this case is characterized by the fact that the mass and stiffness matrices have the embedding property. Consequently, the estimated eigenvalues comply with the inclusion principle, which in turn can be utilized to prove convergence of the approximate solution. The method is applied to a frame

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31

P.-A. Cortat, F., and S. J. Miklavcic. "Fluid drop shape determination by the Rayleigh--Ritz minimization method." ANZIAM Journal 47 (June 26, 2007): 776. http://dx.doi.org/10.21914/anziamj.v47i0.1075.

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32

Deng, Jie, Yuxin Xu, Oriol Guasch, Nansha Gao, and Liling Tang. "Nullspace technique for imposing constraints in the Rayleigh–Ritz method." Journal of Sound and Vibration 527 (June 2022): 116812. http://dx.doi.org/10.1016/j.jsv.2022.116812.

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33

Manuylov, Gaik A. "THE APPROXIMATE SOLUTION FOR PLATES USING MODIFIED RAYLEIGH-RITZ METHOD." International Journal for Computational Civil and Structural Engineering 13, no. 4 (2017): 121–27. http://dx.doi.org/10.22337/2587-9618-2017-13-4-121-127.

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For thin elastic plates of arbitrary shape with a smooth pinched or hinged contour based on the modified Rayleigh-Ritz method, explicit expressions are obtained for the approximate values of the maximum deflection from a uniformly distributed load, the deflection at the point of application of the concentrated force, the critical force of uniform compression, and the first eigenfrequency. The lateral movements were approximated by special functions having level lines similar to the plate contour. The results of calculating the plate in the form of a pear-shaped oval are presented, which are in

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34

Jia, Zhongxiao, and G. W. Stewart. "An analysis of the Rayleigh--Ritz method for approximating eigenspaces." Mathematics of Computation 70, no. 234 (2000): 637–48. http://dx.doi.org/10.1090/s0025-5718-00-01208-4.

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35

Sleijpen, Gerard L. G., Jasper van den Eshof, and Paul Smit. "Optimal a priori error bounds for the Rayleigh-Ritz method." Mathematics of Computation 72, no. 242 (2002): 677–85. http://dx.doi.org/10.1090/s0025-5718-02-01435-7.

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36

Zhu, Lin, and De-Shuang Huang. "A Rayleigh–Ritz style method for large-scale discriminant analysis." Pattern Recognition 47, no. 4 (2014): 1698–708. http://dx.doi.org/10.1016/j.patcog.2013.10.007.

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37

Chakraverty, S., and Laxmi Behera. "Free vibration of non-uniform nanobeams using Rayleigh–Ritz method." Physica E: Low-dimensional Systems and Nanostructures 67 (March 2015): 38–46. http://dx.doi.org/10.1016/j.physe.2014.10.039.

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38

Rinaldi, G., M. Packirisamy, and I. Stiharu. "Dynamic Synthesis of Microsystems Using the Segment Rayleigh–Ritz Method." Journal of Microelectromechanical Systems 17, no. 6 (2008): 1468–80. http://dx.doi.org/10.1109/jmems.2008.2004952.

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39

Grossi, Ricardo Oscar, and Carlos Marcelo Albarracı́n. "Some observations on the application of the Rayleigh–Ritz method." Applied Acoustics 62, no. 10 (2001): 1171–82. http://dx.doi.org/10.1016/s0003-682x(00)00097-9.

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40

Emad, Nahid. "The Padé-Rayleigh-Ritz method for solving large hermitian eigenproblems." Numerical Algorithms 11, no. 1 (1996): 159–79. http://dx.doi.org/10.1007/bf02142494.

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41

Chang, P. C., C. P. Heins, Li Guohao, and Shi Ding. "Seismic study of curved bridges using the Rayleigh-Ritz method." Computers & Structures 21, no. 6 (1985): 1095–104. http://dx.doi.org/10.1016/0045-7949(85)90164-6.

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42

SCHEBLE, MARIO, AGUSTÍN G. RAUSCHERT, and JOSÉ CONVERTI. "AN IMPROVED RAYLEIGH–RITZ SUBSTRUCTURE SYNTHESIS METHOD ADOPTING MIXED COORDINATES." International Journal of Structural Stability and Dynamics 03, no. 04 (2003): 541–65. http://dx.doi.org/10.1142/s021945540300104x.

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This paper presents an improvement of the Rayleigh–Ritz substructure synthesis method that retains all the advantages of the more elaborate existing versions. The displacement field in each component is represented by a set of simple non-admissible shape functions (generalized coordinates). These are subject to a transformation to mixed coordinates (physical and internal). The physical coordinates are defined where necessary to impose boundary conditions and geometrical compatibility. The internal coordinates are chosen in order to optimize the condition number of the matrices involved. Such a

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43

Ganesh, R., and Ranjan Ganguli. "Stiff string approximations in Rayleigh–Ritz method for rotating beams." Applied Mathematics and Computation 219, no. 17 (2013): 9282–95. http://dx.doi.org/10.1016/j.amc.2013.03.017.

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44

Gallistl, D., P. Huber, and D. Peterseim. "On the stability of the Rayleigh–Ritz method for eigenvalues." Numerische Mathematik 137, no. 2 (2017): 339–51. http://dx.doi.org/10.1007/s00211-017-0876-8.

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45

Bhat, R. B. "Rayleigh-Ritz method with separate deflection expressions for structural segments." Journal of Sound and Vibration 115, no. 1 (1987): 174–77. http://dx.doi.org/10.1016/0022-460x(87)90500-1.

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46

Ram, Y. M., S. G. Braun, and J. Blech. "Structural modifications in truncated systems by the Rayleigh-Ritz method." Journal of Sound and Vibration 125, no. 2 (1988): 203–9. http://dx.doi.org/10.1016/0022-460x(88)90279-9.

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47

Arnab, Choudhury, Chandra Samar, Sarkar Susenjit, and Karmakar Mintu. "Analysis of Simply Supported Laminated Composite Plate by Semi Analytical and Finite Element Method for Different Orientation Angles." Strojnícky časopis - Journal of Mechanical Engineering 73, no. 2 (2023): 45–70. http://dx.doi.org/10.2478/scjme-2023-0021.

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Abstract Deflection of simply supported laminated composite plate under transverse load is found out by semi-analytical method (Classical Lamination Theory) and the results are compared with Finite element method using FEA software ANSYS. The equations developed by classical lamination theory for symmetric angle ply and cross ply laminated plate are solved by Navier and Rayleigh-Ritz method. The efficiency of Navier and Rayleigh-Ritz method in solving the problems of symmetric angle ply and cross ply laminated plate are investigated by comparing their results with ANSYS. Percentage error of th

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48

Stamatelos, Dimitrios G., and George N. Labeas. "Buckling Analysis of Laminated Stiffened Plates with Material Anisotropy Using the Rayleigh–Ritz Approach." Computation 11, no. 6 (2023): 110. http://dx.doi.org/10.3390/computation11060110.

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An energy-based solution for calculating the buckling loads of partially anisotropic stiffened plates is presented, such as antisymmetric cross-ply and angle-ply laminations. A discrete approach, for the mathematical modelling and formulations of the stiffened plates, is followed. The developed formulations extend the Rayleigh–Ritz method and explore the available anisotropic unstiffened plate buckling solutions to the interesting cases of stiffened plates with some degree of material anisotropy. The examined cases consider simply supported unstiffened and stiffened plates under uniform and li

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49

Meirovitch, Leonard, and Moon K. Kwak. "Convergence of the classical Rayleigh-Ritz method and the finite element method." AIAA Journal 28, no. 8 (1990): 1509–16. http://dx.doi.org/10.2514/3.25246.

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50

Shi, Wenya, and Zhixiang Chen. "A breakdown-free block conjugate gradient method for large-scale discriminant analysis." AIMS Mathematics 9, no. 7 (2024): 18777–95. http://dx.doi.org/10.3934/math.2024914.

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<abstract><p>Rayleigh-Ritz discriminant analysis (RRDA) is an effective algorithm for linear discriminant analysis (LDA), but there are some drawbacks in its implementation. In this paper, we first improved Rayleigh-Ritz discriminant analysis (IRRDA) to make its framework more concise, and established the equivalence theory of the solution space between our discriminant analysis and RRDA. Second, we proposed a new model based on positive definite systems of linear equations for linear discriminant analysis, and certificated the rationality of the new model. Compared with the tradit

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