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In the finite element method context, mathematically the same algorithm is commonly called the Ritz-Galerkin method. The Rayleigh–Ritz method or Ritz method terminology is typical in mechanical and structural engineering to approximate the eigenmodes and resonant frequencies of a structure.
Walther Heinrich Wilhelm Ritz (22 February 1878 – 7 July 1909) was a Swiss theoretical physicist. He is most famous for his work with Johannes Rydberg on the Rydberg–Ritz combination principle. Ritz is also known for the variational method named after him, the Ritz method.
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The outcome of the Rayleigh–Ritz method is determined by the subspace spanned by all columns of matrices ,, and , where a basis of the subspace can theoretically be arbitrary. However, in inexact computer arithmetic the Rayleigh–Ritz method becomes numerically unstable if some of the basis vectors are approximately linearly dependent.
The variational method of Ritz would found his use quantum mechanics with the development of Hellmann–Feynman theorem. The theorem was first discussed by Schrödinger in 1926, the first proof was given by Paul Güttinger in 1932, and later rediscovered independently by Wolfgang Pauli and Hans Hellmann in 1933, and by Feynman in 1939.
Ritz Newspaper, sometimes Ritz Magazine, a defunct UK fashion and gossip periodical; Ritz Video, a chain of video rental stores in the United Kingdom that was bought out by Blockbuster; Maruti Suzuki Ritz, the Indian version of the Suzuki Splash, a hatchback city car; Rydberg–Ritz combination principle; Ritz method (mathematics)
The Ritz method, [9] based on the shell theory, [10] is frequently utilised for dynamic analysis of carbon nanotubes (CNTs). The Ritz method, connected to Hamilton's principle, is employed to determine the equilibrium state and minimize the energy functional of a conservative structural system undergoing kinematically admissible growth or deformation.
The Rayleigh–Ritz method for solving boundary-value problems in elasticity and wave propagation; Fermat's principle in geometrical optics; Hamilton's principle in classical mechanics; Maupertuis' principle in classical mechanics; The principle of least action in mechanics, electromagnetic theory, and quantum mechanics; The variational method ...