Solving Critical Point Conditions for the Hamming and Taxicab Distances to Solution Sets of Polynomial Equations
2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)(2019)
摘要
Minimizing the Euclidean distance (ℓ
2
-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
0
-"norm") and taxicab distance (ℓ
1
-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.
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关键词
Numerical algebraic geometry,real solutions,Hamming distance,taxicab distance,critical points
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