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

31 May 2013 Use of formal derivative for extremizing real-valued functions of complex variables

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

Proceedings Volume 8720, Photonic Applications for Aerospace, Commercial, and Harsh Environments IV; 87200H (2013) https://doi.org/10.1117/12.2016270
Event: SPIE Defense, Security, and Sensing, 2013, Baltimore, Maryland, United States

Abstract

The extremum of a real-valued nonanalytic function of a complex variable that defies Cauchy-Riemann equations 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.

Citation Download Citation

Sudarshan R. Nelatury, Charles W. Nelatury, and Charles F. Nelatury "Use of formal derivative for extremizing real-valued functions of complex variables", Proc. SPIE 8720, Photonic Applications for Aerospace, Commercial, and Harsh Environments IV, 87200H (31 May 2013); https://doi.org/10.1117/12.2016270

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