Iterated Exponentiation, Matrix-Matrix Exponentiation, and Entropy
نویسندگان
چکیده
منابع مشابه
Matrix Exponentiation and the Frank-Kamenetskii Equation
Long time solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivatives are approximated by high-order finite difference approximations. A forward difference approximation to the time derivative leads to a Lawson-Euler scheme. Computations performed with a BDF approximation to the time der...
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متن کاملOn the Convergence of Iterated Exponentiation—11*
1. A. F. Horadam. "Basic Properties of a Certain Generalized Sequence of Numbers." The Fibonacci Quarterly 3 (1965):161-75. 2. A. F. Horadam. "Complex Fibonacci Numbers and Fibonacci Quaternions." Amer. Math. Monthly 70 (1963):289-91. 3. A. L. Iakin. "Generalized Quaternions with Quaternion Components." The Fibonacci Quarterly 15 (1977):35Q-52. 4. A. L. Iakin. "Generalized Quaternions of Higher...
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(2) f(x) E F(x9 x)9 i.e., the case of Eq. (1) where x = y. For both Eqs. (1) and (2), the ordering of the exponentiations is important, and for Eq. (1) and throughout this paper, we mean a bracketing order "from the top down," i.e., x raised to the power y9 followed by y raised to the power x^, and then x raised to the power y^\ and so on, all the way down to the x which is at the lowest positi...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1994
ISSN: 0022-247X
DOI: 10.1006/jmaa.1994.1132