Topic
Multicomplex number
About: Multicomplex number is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 9 citations. The topic is also known as: Multicomplex number.
Papers
TL;DR: In this paper, a multicomplex Riemann zeta function is defined through analytic continuation, and properties of this function are explored, and the authors are able to state a multic-mplex equivalence to the riemann hypothesis.
Abstract: After reviewing properties of analytic functions on the multicomplex number space $${\mathbb{C}_{k}}$$
(a commutative generalization of the bicomplex numbers $${\mathbb{C}_{2}}$$
), a multicomplex Riemann zeta function is defined through analytic continuation. Properties of this function are explored, and we are able to state a multicomplex equivalence to the Riemann hypothesis.
4 citations
TL;DR: A Matlab class for multicomplex numbers was developed with particular attention paid to the robust and accurate handling of small imaginary components to allow the class to be used to obtain n-order derivative information using the multicamplex step method for, among other applications, gradient-based optimization and optimum control problems.
Abstract: A Matlab class for multicomplex numbers was developed with particular attention paid to the robust and accurate handling of small imaginary components. This is primarily to allow the class to be used to obtain n-order derivative information using the multicomplex step method for, among other applications, gradient-based optimization and optimum control problems. The algebra of multicomplex numbers is described, as is its accurate computational implementation, considering small term approximations and the identification of principal values. The implementation of the method in Matlab is studied, and a class definition is constructed. This new class definition enables Matlab to handle n-order multicomplex numbers and perform arithmetic functions. It was found that with this method, the step size could be arbitrarily decreased toward machine precision. Use of the method to obtain up to the seventh derivative of functions is presented, as is timing data to demonstrate the efficiency of the class implementation.
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2013 | 1 |