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Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns
Solving Quadratic Equations PhaseLift Many Equations Unknowns
2015/6/17
This note shows that we can recover any complex vector x0 ∈ Cn exactly from on the order of n quadratic equations of the form |hai, x0i|2 = bi, i = 1, . . . , m, by using a semidefinite program known ...
Linear estimates for solutions of quadratic equations in free groups
Linear estimates solutions of quadratic equations Group Theory
2011/9/6
Abstract: We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by $2s$ for orientable equation and by $12s^4$ for no...
A polynomial bound on solutions of quadratic equations in free groups
polynomial bound quadratic equations free groups Group Theory
2011/8/31
Abstract: We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutio...
Geodesic diameter of sets defined by few quadratic equations and inequalities
Geodesic diameter of sets defined quadratic equations nequalities
2010/11/29
We prove a bound for the geodesic diameter of a subset of the unit ball in Rn described by a fixed number of quadratic equations and inequalities,which is polynomial in n, whereas the known bound for ...