Use of formal derivative for extremizing real-valued functions of complex variables

Sudarshan R. Nelatury; Charles W. Nelatury; Charles F. Nelatury

doi:10.1117/12.2016270

Use of formal derivative for extremizing real-valued functions of complex variables

Sudarshan R. Nelatury, Charles W. Nelatury, Charles F. Nelatury

School of Engineering (Behrend)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The extremum of a real-valued nonanalytic function of a complex variable that defies Cauchy-Riemann equa- tions can be found using formal derivatives. This letter shows how the first and second derivative tests can be recast via formal gradient and formal Hessian. The elegance of the method is illustrated with examples.

Original language	English (US)
Title of host publication	Photonic Applications for Aerospace, Commercial, and Harsh Environments IV
DOIs	https://doi.org/10.1117/12.2016270
State	Published - 2013
Event	Photonic Applications for Aerospace, Commercial, and Harsh Environments IV - Baltimore, MD, United States Duration: Apr 29 2013 → May 1 2013

Publication series

Name	Proceedings of SPIE - The International Society for Optical Engineering
Volume	8720
ISSN (Print)	0277-786X
ISSN (Electronic)	1996-756X

Other

Other	Photonic Applications for Aerospace, Commercial, and Harsh Environments IV
Country/Territory	United States
City	Baltimore, MD
Period	4/29/13 → 5/1/13

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
Condensed Matter Physics
Computer Science Applications
Applied Mathematics
Electrical and Electronic Engineering

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10.1117/12.2016270

Cite this

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title = "Use of formal derivative for extremizing real-valued functions of complex variables",

abstract = "The extremum of a real-valued nonanalytic function of a complex variable that defies Cauchy-Riemann equa- tions can be found using formal derivatives. This letter shows how the first and second derivative tests can be recast via formal gradient and formal Hessian. The elegance of the method is illustrated with examples.",

author = "Nelatury, {Sudarshan R.} and Nelatury, {Charles W.} and Nelatury, {Charles F.}",

year = "2013",

doi = "10.1117/12.2016270",

language = "English (US)",

isbn = "9780819495112",

series = "Proceedings of SPIE - The International Society for Optical Engineering",

booktitle = "Photonic Applications for Aerospace, Commercial, and Harsh Environments IV",

note = "Photonic Applications for Aerospace, Commercial, and Harsh Environments IV ; Conference date: 29-04-2013 Through 01-05-2013",

}

Nelatury, SR, Nelatury, CW & Nelatury, CF 2013, Use of formal derivative for extremizing real-valued functions of complex variables. in Photonic Applications for Aerospace, Commercial, and Harsh Environments IV., 87200H, Proceedings of SPIE - The International Society for Optical Engineering, vol. 8720, Photonic Applications for Aerospace, Commercial, and Harsh Environments IV, Baltimore, MD, United States, 4/29/13. https://doi.org/10.1117/12.2016270

Use of formal derivative for extremizing real-valued functions of complex variables. / Nelatury, Sudarshan R.; Nelatury, Charles W.; Nelatury, Charles F.
Photonic Applications for Aerospace, Commercial, and Harsh Environments IV. 2013. 87200H (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8720).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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PY - 2013

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Use of formal derivative for extremizing real-valued functions of complex variables

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