Ikke glem «total sum of squares»

The Sum of Two Squares

A 'sum of Squares' Theorem for Visibility Complexes a 'sum of Squares' Theorem for Visibility Complexes

We present a new and simpler method to implement in constant amortized time the ip operation of the so-called 'Greedy Flip Algorithm', an optimal algorithm to compute the visibility graph/complex of a collection of pairwise disjoint bounded convex sets of constant complexity. The method uses only the incidence structure of the visibility complex and only the primitive predicate which states tha...

GLOBAL TOTAL LEAST SQUARES Global Total Least Squares

A method for the construction of open approximate models from vector time series Preface PhD research is a largely open proces in which a stimulating environment plays a crucial role. I am indebted to several people and institutions that shaped such an environment for me during the years since April 1990. First and for all, I would like to thank my supervisor, Christiaan Heij. He set me on the ...

Controls Applications of Sum of Squares Programming

We consider nonlinear systems with polynomial vector fields and pose two classes of system theoretic problems that may be solved by sum of squares programming. The first is disturbance analysis using three different norms to bound the reachable set. The second is the synthesis of a polynomial state feedback controller to enlarge the provable region of attraction. We also outline a variant of th...

The Sum of Digits Function of Squares

We consider the set of squares n2, n < 2k, and split up the sum of binary digits s(n2) into two parts s[<k](n 2) + s[≥k](n 2), where s[<k](n 2) = s(n2 mod 2k) collects the first k digits and s[≥k](n 2) = s(bn2/2kc) collects the remaining digits. We present very precise results on the distribution on s[<k](n 2) and s[≥k](n 2). For example, we provide asymptotic formulas for the numbers #{n < 2k ...