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On semi-exponential Gauss–Weierstrass operators

Analysis and Mathematical Physics, 2022
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Vijay Gupta, Ali Aral
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Exponentiating a Bundle of Linear Operators

Set-Valued Analysis, 2006
Let \(X\) be a real Banach space, \(L(X)\) the space of all linear continuous operators from \(X\) to \(X\), endowed with its sup norm, let \(\Xi\subseteq L(X)\) and let \(F:X\rightrightarrows X\), given by \(F(x)=\{Ax \mid A\in \Xi\}\) for each \(x\in X\).
Amri, Amine, Seeger, Alberto
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Multivariate Exponential Operators

Studies in Applied Mathematics, 1980
An unexpected connection between a certain class of exponential approximation operators and polynomial sequences of binomial type was discovered by Ismail. Building on this result, we present a multivariate analogue of these exponential operators.
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Preconditioning the Matrix Exponential Operator with Applications

Journal of Scientific Computing, 1998
The paper deals with two classes for preconditioning the matrix exponential operator \(e^Ay_0\). The first technique reduces the computation of the exponential operator for problems of approximation of an integral involving the exponential of a preconditioner for \(A\) and this integral is approximated by means of Krylov subspace approximations.
Paul Castillo 0001, Yousef Saad
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Positive linear operators and exponential functions

Mathematical Foundations of Computing, 2023
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Ioan Rasa
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New method for merging several exponential operators’ product into one exponential operator

Modern Physics Letters A, 2023
For two operators [Formula: see text] and [Formula: see text] which obey [Formula: see text]we shall prove [Formula: see text]which means we want to merge two exponential operators’ product into one exponential operator. This kind of operator identity is useful for calculating the quantum entropy [Formula: see text] since [Formula: see text] when ...
Chun-Zao Zhang, Hong-Yi Fan
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Adaptive application of the operator exponential

Journal of Numerical Mathematics, 2006
The author studies the approximation of the exponential of a sectorial operator by a parallel algorithm that is based upon the quadrature of the integral representation of the operator exponential and the solution of elliptic problems. The method allows in particular the solution of initial value problems for linear evolution equations with arbitrarily
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Averaging operators for exponential splittings

Numerische Mathematik, 2007
Given a matrix \(M\in{\mathbb C}^{n\times n}\), the author considers the averaging of \(M\) defined as \[ A=(1/k)\sum_{j=0}^{k-1} J^jMJ^{-j}, \] where \(J\in{\mathbb C}^{n\times n}\) is a unipotent matrix, that is, \(J^k=I\) for some smallest \(k\in{\mathbb N}\).
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Fast exponentiation using the truncation operation

Computational Complexity, 1992
A tight bound of \(\Theta(\sqrt k)\) time required to compute \(2^{2^ k}\) is proved for the inputs: integer \(k\) and arbitrary integer greater than \(2^{2^ k}\), the operations \(+,-,*,/,\lfloor\cdot\rfloor,\leq\) and constants \(\{0,1\}\). It is applied to the algorithms: (1) for computing \(\lfloor\log\log a\rfloor\) for all \(n\)-bit integers \(a\)
Nader H. Bshouty, Yishay Mansour, Baruch Schieber, Prasoon Tiwari   +3 more
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Pointwise Estimate for Exponential-Type Operators

Southeast Asian Bulletin of Mathematics, 2000
The authors obtain a pointwise estimate for three general exponential-type operators by using the concept of Ditzian-Totik modulus of smoothness.
Song, Zhanjie, Liu, Xiwu, Guo, Shunsheng
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