Greenbaum, AnneChoi, Daeshik2013-11-142013-11-142013-11-142013Choi_washington_0250E_12162.pdfhttp://hdl.handle.net/1773/24332Thesis (Ph.D.)--University of Washington, 2013We study Crouzeix's conjecture: for any polynomial p and any square matrix A, the spectral norm of the matrix p(A) is at most double of the supremum norm of the polynomial p on the numerical range of the matrix A.application/pdfen-USCopyright is held by the individual authors.Crouzeix's conjecture; Field of values; GMRES; Jordan block; K-spectral set; Numerical rangeMathematicsmathematicsThesis