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Robust Plotting of Generalized Lemniscates by Rida T. Farouki; Chang Yong Han is a Engineering article available to read on EtoBox.

What is Robust Plotting of Generalized Lemniscates about?

A root neighborhood (or pseudozero set) of a degree-n polynomial p(z) is the set of roots of all polynomials p(z) whose coefficients differ from those of p(z), under a specified norm in C n+1 , by no more than a given amount ε. In the case of a weighted infinity norm, root neighborhoods are bounded by generalized lemniscates (algebraic curves of degree 4n). A simple description of generalized lemniscates may be cast in terms of multipolar coordinates: namely, the product of the distances r 1 , . . . , r n of a variable point z from the n roots z 1 , . . . , z n of p(z) is equal to a degree-n polynomial in the distance r of z from the origin (in the case of "ordinary" lemniscates, this polynomial specializes to a constant). The ability to efficiently and faithfully graph lemniscates is important in numerical analysis, control theory, and other scientific/engineering applications. By constructing the tensor-product Bernstein form over a bounding rectangle, we develop a robust adaptive algorithm to plot lemniscates, employing quadtree subdivision to efficiently achieve any desired resolution. Moreover, singular points of the lemniscate (if any) may be explicitly identified and incorpo

Who reads Robust Plotting of Generalized Lemniscates?

Author

Rida T. Farouki; Chang Yong Han

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0168-9274)

Published

2004

Language

EN

Field

Engineering (Physical Sciences)