Name
Title | ||
|---|---|---|
Solving Critical Point Conditions for the Hamming and Taxicab Distances to Solution Sets of Polynomial Equations |
Abstract | ||
|---|---|---|
Minimizing the Euclidean distance (ℓ
<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>
-norm) from a given point to the solution set of a given system of polynomial equations can be accomplished via critical point techniques. This article extends critical point techniques to minimization with respect to Hamming distance (ℓ
<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>
-"norm") and taxicab distance (ℓ
<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub>
-norm). Numerical algebraic geometric techniques are derived for computing a finite set of real points satisfying the polynomial equations which contains a global minimizer. Several examples are used to demonstrate the new techniques. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1109/SYNASC49474.2019.00017 | 2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) |
Keywords | DocType | ISSN |
Numerical algebraic geometry,real solutions,Hamming distance,taxicab distance,critical points | Conference | 2470-8801 |
ISBN | Citations | PageRank |
978-1-7281-5725-2 | 0 | 0.34 |
References | Authors | |
6 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Danielle A. Brake | 1 | 0 | 0.34 |
| Noah S. Daleo | 2 | 0 | 0.34 |
| Jonathan D. Hauenstein | 3 | 269 | 37.65 |
| Samantha N. Sherman | 4 | 0 | 0.34 |