A Universal Bound for the Average Cost of Root Finding (2009)
Kim, Myong-Hi, Martens, Marco, Sutherland, Scott
We analyze a path-lifting algorithm for finding an approximate zero of a complex polynomial, and show that for any polynomial with distinct roots in the unit disk, the average number of iterates this...
Implicit Gamma Theorems (I): (2007)
J. P. Dedieu, M. Shub, F. Tisseur, Jean-pierre Dedieu, Myong-hi Kim, ...
Hilbert
Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra (2007)
Jean-pierre Dedieu, Myong-hi Kim, Michael Shub
Let g : E F be an analytic function between two Hilbert spaces E and F. We study the set g(B(x, #)) F, the image under g of the closed ball about x E with radius #. When g(x) expresses the solution...
Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra (2003)
Dedieu, Jean-Pierre, Kim, Myong-Hi, Shub, Michael, Tisseur, Françoise
Let g : E → F be an analytic function between two Hilbert spaces E and F. We study the set g(B(x, ε)) ⊂ E, the image under g of the closed ball about x∈ E with radius ε . When g(x) expresses...
Jean-pierre Dedieu, Myong-hi Kim, Michael Shub, Françoise Tisseur
Abstract. Let g: E → F be an analytic function between two Hilbert spaces E and F. We study the set g(B(x,ε)) ⊂ F, the image under g of the closed ball about x ∈ E with radius ε. When g(x)...
Polynomial root-finding algorithms and branched covers (1991)
Kim, Myong-Hi, Sutherland, Scott
We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree $d$ with a path-lifting algorithm for finding individual roots. In particular,...
Computational complexity of the Euler algorithms for the roots of complex polynomials / (1986)
"A dissertation submitted to the Graduate Faculty in Mathematics ... "