| Review: |
This textbook provides a comprehensive treatment of numerical polynomial algebra, an area that falls between classical numerical analysis and computer algebra. It introduces a conceptual framework that allows the meaningful solution of various algebraic problems that have multivariate polynomial equations with coefficients with some indeterminacy. This involves a combination of numerical linear algebra and commutative algebra. The book also provides a survey of polynomial problems in scientific computing that can be solved numerically and a guide to their numerical treatment. There are chapters on: polynomials; representations of polynomial ideals; polynomials with coefficients of limited accuracy; approximate numerical computation; univariate polynomials; various tasks with empirical univariate polynomials; one multivariate polynomial; zero-dimensional systems of multivariate polynomials; systems of empirical multivariate polynomials; numerical basis computation; and matrix eigenproblems for positive-dimensional systems. |