The Condition of Polynomials in Power Form

DOI10.2307/2006047zbMath0399.41002OpenAlexW4252648814MaRDI QIDQ4183740

Walter Gautschi

Publication date: 1979

Full work available at URL: https://doi.org/10.2307/2006047

zbMATH Keywords

Numerical ConditionParametrization of PolynomialsPower Basis

Mathematics Subject Classification ID

Roundoff error (65G50) Approximation by polynomials (41A10) Numerical approximation and computational geometry (primarily algorithms) (65D99)

Related Items (18)

On the best conditioned bases of quadratic polynomials ⋮ On the numerical condition of polynomials in Bernstein form ⋮ Stability of finite linear combinations of vectors under changes of their coefficients. An application to approximation problems ⋮ A comparison of companion matrix methods to find roots of a trigonometric polynomial ⋮ Correcting Three Errors in Kantorovich & Krylov′s <em>Approximate Methods of Higher Analysis</em> ⋮ Using parity to accelerate Hermite function computations: zeros of truncated Hermite series, Gaussian quadrature and Clenshaw summation ⋮ Eight Perspectives on the Exponentially Ill-Conditioned Equation $\varepsilon y - x y' + y = 0$ ⋮ The numerical solution of fractional integral equations via orthogonal polynomials in fractional powers ⋮ On the generation of Krylov subspace bases ⋮ On condition numbers of a basis ⋮ Fehlerabschaetzungen für Koeffizienten von Exponentialsummen und Polynomen ⋮ Deviations of discrete distributions and a question of Móri ⋮ Chebyshev-Vandermonde Systems ⋮ A Chebychev-Vandermonde solver ⋮ Direct operatorial tau method for pantograph-type equations ⋮ Perturbation bounds for polynomials ⋮ An adaptive \(s\)-step conjugate gradient algorithm with dynamic basis updating. ⋮ A Newton basis for kernel spaces

Cites Work

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• Norm estimates for inverses of Vandermonde matrices
• A Theory of Condition
• The Condition of Orthogonal Polynomials

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