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<p>We deal with root separation of a real polynomial. We bound the spread of a given polynomial, and we bound the roots of a polynomial whose roots are the differences of the roots of the initial polynomial. Intensive use of matricial norms (and matrix norms) is made. Extensions and ameliorations of the Leverrier-Faddeev algorithm and of the Caley-Hamilton theorem are mentioned.</p>

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POLYNOMIALS WHOSE ROOTS ARE THE DIFFERENCES OF THE ROOTS OF A GIVEN POLYNOMIAL

  • 期刊论文

  • 发表日期：

    2025年1月15日

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  • M. A. Facas Vicente,
  • José Vitória

摘要

We deal with root separation of a real polynomial. We bound the spread of a given polynomial, and we bound the roots of a polynomial whose roots are the differences of the roots of the initial polynomial. Intensive use of matricial norms (and matrix norms) is made. Extensions and ameliorations of the Leverrier-Faddeev algorithm and of the Caley-Hamilton theorem are mentioned.