Hyperbolic Polynomials and Convex Analysis

By Heinz H. Bauschke, Osman Güler, A. S. Lewis, Hristo S. Sendov. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2001

146 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d01d447b49d78960e273bd0fc0bf337bde88747f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Petter Brand'en
2. Adam W. Marcus
3. Julius Borcea
4. Daniel A. Spielman
5. Nikhil Srivastava
6. Thomas M. Liggett
7. Pablo A. Parrilo
8. Victor Vinnikov

In Computational Theory and Mathematics

1. Petter Brand'en
2. Adam W. Marcus
3. Nikhil Srivastava
4. Daniel A. Spielman
5. Julius Borcea
6. Victor Vinnikov
7. Pablo A. Parrilo
8. Thomas M. Liggett

In Numerical Analysis

1. Petter Brand'en
2. Nikhil Srivastava
3. Adam W. Marcus
4. Julius Borcea
5. Victor Vinnikov
6. Pablo A. Parrilo
7. Daniel A. Spielman
8. A. S. Lewis

Citations in the corpus

• The lax conjecture is true (2003, background): “For more details on these reasons, see [6, 1].”
• Sharp isoperimetric inequalities via the ABP method (2013, unknown): “(this follows by induction from the first statement in example (i); see also [2]), or the polynomial det(X) in the convex cone of symmetric positive definite matrices —which we consider in the space R.”
• Negative dependence and the geometry of polynomials (2007, background): “Recently, hyperbolic polynomials have proved to be quite useful in other areas of mathematics such as convex optimization [4, 36], complex analysis [7], matrix theory and combinatorics [34, 35].”
• LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future (2012, background): “eous setting (convex cones). In the homogeneous setting, RZ polynomials correspond to hyperbolic polynomials and rigidly convex algebraic interiors correspond to their hyperbolicity cones, see, e.g., [17, 18, 36, 44, 21, 7, 50]. Theorem 3.1 then provides a solution the Lax conjecture concerning homo”
• Interlacing families II: Mixed characteristic polynomials and the Kadison{Singer problem (2013, methodology): “There are other ways of proving Lemma 5.7 that go through more elementary techniques than those used by Helton and Vinnikov [HV07]. James Renegar has pointed out that it follows from Corollary 4.6 of [BGLS01]. Terence Tao [Tao13] has also presented a more elementary proof. Recall that we are interes”