First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also determine minimal structured perturbations for which approximate eigenelements are exact eigenelements of the perturbed polynomials. Next, we analyze the effect of structure preserving linearizations of structured matrix polynomials on the structured backward errors of approximate eigenelements. We identify structure preserving linearizations which have almost no adverse effect on the structured backward errors of approximate eigenelements of the polynomials. Finally, we analyze structured pseudospectra of a structured matrix polynomial and establish a partial equality between unstructured and structured pseudospectra.
Conditioning and backward error of block-symmetric block-tridiagonal linearizations of matrix polynomials
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Universidad Carlos III de Madrid（马德里卡洛斯三世大学）；Universidade de Lisboa（里斯本大学）；Faculdade de Economia do Porto（波尔图经济与管理学院）；Boston University（波士顿大学）
Fast and backward stable computation of the eigenvalues and eigenvectors of matrix polynomials
Instituto de Ciencias Matemáticas, Universidad Autónoma de Madrid（马德里自治大学数学科学研究所）；Nazarbayev University（纳扎尔巴耶夫大学）；ISTI, Area della ricerca CNR（意大利国家研究委员会ISTI研究所）；KU Leuven（荷语鲁汶大学）；Washington State University（华盛顿州立大学）
A unified approach to Fiedler-like pencils via strong block minimal bases pencils
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Universidad Carlos III de Madrid（马德里卡洛斯三世大学）；KU Leuven（荷语鲁汶大学）；Dos Pueblos High School（多斯普埃洛高中）；University of Virginia（弗吉尼亚大学）
