# arithmetic operations

(0.001 seconds)

## 8 matching pages

##### 2: Bibliography K
• C. Kormanyos (2011) Algorithm 910: a portable C++ multiple-precision system for special-function calculations. ACM Trans. Math. Software 37 (4), pp. Art. 45, 27.
• ##### 3: 3.1 Arithmetics and Error Measures
The elementary arithmetical operations on intervals are defined as follows: …
##### 4: Bibliography H
• B. Hayes (2009) The higher arithmetic. American Scientist 97, pp. 364–368.
• G. J. Heckman (1991) An elementary approach to the hypergeometric shift operators of Opdam. Invent. Math. 103 (2), pp. 341–350.
• C. Hunter (1981) Two Parametric Eigenvalue Problems of Differential Equations. In Spectral Theory of Differential Operators (Birmingham, AL, 1981), North-Holland Math. Stud., Vol. 55, pp. 233–241.
• ##### 5: 18.39 Applications in the Physical Sciences
The fundamental quantum Schrödinger operator, also called the Hamiltonian, $\mathcal{H}$, is a second order differential operator of the form … Analogous to (18.39.7) the 3D Schrödinger operator is …where $\mathrm{L}^{2}$ is the (squared) angular momentum operator (14.30.12). … Here tridiagonal representations of simple Schrödinger operators play a similar role. The radial operator (18.39.28) …
##### 6: 3.6 Linear Difference Equations
3.6.2 $a_{n}\Delta^{2}w_{n-1}+(2a_{n}-b_{n})\Delta w_{n-1}+(a_{n}-b_{n}+c_{n})w_{n-1}% =d_{n},$
where $\Delta w_{n-1}=w_{n}-w_{n-1}$, $\Delta^{2}w_{n-1}=\Delta w_{n}-\Delta w_{n-1}$, and $n\in\mathbb{Z}$. … Unless exact arithmetic is being used, however, each step of the calculation introduces rounding errors. …
##### 7: Bibliography M
• I. Marquette and C. Quesne (2013) New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems. J. Math. Phys. 54 (10), pp. Paper 102102, 12 pp..
• A. Máté, P. Nevai, and W. Van Assche (1991) The supports of measures associated with orthogonal polynomials and the spectra of the related selfadjoint operators. Rocky Mountain J. Math. 21 (1), pp. 501–527.
• D. W. Matula and P. Kornerup (1980) Foundations of Finite Precision Rational Arithmetic. In Fundamentals of Numerical Computation (Computer-oriented Numerical Analysis), G. Alefeld and R. D. Grigorieff (Eds.), Comput. Suppl., Vol. 2, Vienna, pp. 85–111.
• X. Merrheim (1994) The computation of elementary functions in radix $2^{p}$ . Computing 53 (3-4), pp. 219–232.
• mpmath (free python library)
• ##### 8: Bibliography C
• C. W. Clenshaw, F. W. J. Olver, and P. R. Turner (1989) Level-Index Arithmetic: An Introductory Survey. In Numerical Analysis and Parallel Processing (Lancaster, 1987), P. R. Turner (Ed.), Lecture Notes in Math., Vol. 1397, pp. 95–168.
• D. A. Cox (1984) The arithmetic-geometric mean of Gauss. Enseign. Math. (2) 30 (3-4), pp. 275–330.
• D. A. Cox (1985) Gauss and the arithmetic-geometric mean. Notices Amer. Math. Soc. 32 (2), pp. 147–151.
• H. L. Cycon, R. G. Froese, W. Krisch, and B. Simon (2008) Schrödinger Operators, with Applications to Quantum Mechanics and Global Geometry. Springer Verlag, New York.