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1: 3.6 Linear Difference Equations
Then w n is said to be a recessive (equivalently, minimal or distinguished) solution as n , and it is unique except for a constant factor. … …
2: 37.20 Mathematical Applications
Numerical Solution of Differential Equations
OPs are used in collocation method or spectral method for numerical solution of partial differential equations. … A minimal cubature rule is a numerical integration rule that uses the smallest number of nodes among cubature rules of the same degree. …Although Gaussian cubature rules rarely exist and they do not exist for centrally symmetric domains, minimal or near minimal cubature rules on the unit square are known and provide efficient numerical integration rules. …
3: Bibliography S
  • H. Segur and M. J. Ablowitz (1981) Asymptotic solutions of nonlinear evolution equations and a Painlevé transcendent. Phys. D 3 (1-2), pp. 165–184.
  • N. Seiberg and D. Shih (2005) Flux vacua and branes of the minimal superstring. J. High Energy Phys. 2005 (01), pp. 1–37.
  • R. Shail (1978) Lamé polynomial solutions to some elliptic crack and punch problems. Internat. J. Engrg. Sci. 16 (8), pp. 551–563.
  • R. B. Shirts (1993a) The computation of eigenvalues and solutions of Mathieu’s differential equation for noninteger order. ACM Trans. Math. Software 19 (3), pp. 377–390.
  • R. Spigler (1984) The linear differential equation whose solutions are the products of solutions of two given differential equations. J. Math. Anal. Appl. 98 (1), pp. 130–147.
  • 4: 3.11 Approximation Techniques
    Then there exists a unique n th degree polynomial p n ( x ) , called the minimax (or best uniform) polynomial approximation to f ( x ) on [ a , b ] , that minimizes max a x b | ϵ n ( x ) | , where ϵ n ( x ) = f ( x ) p n ( x ) . … of type [ k , ] to f on [ a , b ] minimizes the maximum value of | ϵ k , ( x ) | on [ a , b ] , where … With b 0 = 1 , the last q equations give b 1 , , b q as the solution of a system of linear equations. … that minimizesof given functions ϕ k ( x ) , k = 0 , 1 , , n , that minimizes
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