1997
DOI: 10.1006/hmat.1996.2146
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The Origin of the Method of Steepest Descent

Abstract: The method of steepest descent, also known as the saddle-point method, is a natural development of Laplace's method applied to the asymptotic estimate of integrals of analytic functions. Mathematicians have often attributed the method of steepest descent to the physicist Peter Debye, who in 1909 worked it out in an asymptotic study of Bessel functions. Debye himself remarked that he had borrowed the idea of the method from an 1863 paper of Bernhard Riemann. The present article offers a detailed historical anal… Show more

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Cited by 134 publications
(79 citation statements)
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“…[8] For the removal of initial steric clashes, 5000-steps energy minimization is performed for each system using the steepest descent method. [41] Subsequently, a 200 ps equilibration in NVT ensemble is performed to equilibrate each system at 310 K and to avoid any kind of void formation in the box followed by a 5 ns equilibration at isothermal-isobaric (NPT) ensemble to attain a steady pressure of 1 atm. This period of equilibration is found to be sufficient enough for the convergence of properties like pressure, temperature for each system.…”
Section: Simulation Detailsmentioning
confidence: 99%
“…[8] For the removal of initial steric clashes, 5000-steps energy minimization is performed for each system using the steepest descent method. [41] Subsequently, a 200 ps equilibration in NVT ensemble is performed to equilibrate each system at 310 K and to avoid any kind of void formation in the box followed by a 5 ns equilibration at isothermal-isobaric (NPT) ensemble to attain a steady pressure of 1 atm. This period of equilibration is found to be sufficient enough for the convergence of properties like pressure, temperature for each system.…”
Section: Simulation Detailsmentioning
confidence: 99%
“…[22] Before MD simulations, the complexes were gradually relaxed using 10 000 cycles of minimization (500 cycles of steepest descent [23,24] and 9500 cycles of conjugate gradient minimization [25] ). The general CHARMM36 force was used to generate the force field parameters for protein and ligands.…”
Section: Computational Studiesmentioning
confidence: 99%
“…A constant temperature and pressure for the whole system (300 K and 1 bar) was achieved with the Berendsen thermostat [25] and the Parrinello and Rahman [26] barostat parameters. Steepest descent energy minimization process [27] was utilized to minimize the simulated system step-by-step until a tolerance of 1000 kJ/mol was achieved. A pH of 7 was maintained for all the molecular dynamics simulation processes.…”
Section: Molecular Dynamics Simulationmentioning
confidence: 99%