Polynomial Norms

Non-polynomial Spline Method for Solving Coupled Burgers Equations

In this paper, non-polynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using Von-Neumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equation...

VARYING DEGREE POLYNOMIAL REGRESSION * I . RATES OF CONVERGENCE ( Abbreviated Title : VARYING DEGREE POLYNOMIAL REGRESSION

For a regression model Yt = gO(x t) + e t , the unknown function gO is estimated consistently using varying degree polynomial regression. Consistency is with respect to a class of norms similar to weighted Sobolev norms, and the method of proof involves metric entropy calculations that enable the development of rates of convergence in these norms. The estimator is viewed as the solution to some...

L norms of trigonometric polynomials

Solving the Closest Vector Problem with respect to ℓp Norms

We present deterministic polynomially space bounded algorithms for the closest vector problem for all lp-norms, 1 < p < ∞, and all polyhedral norms, in particular for the l1norm and the l∞-norm. For all lp-norms with 1 < p < ∞ the running time of the algorithm is p · log2(r)n, where r is an upper bound on the size of the coefficients of the target vector and the lattice basis and n is the dimen...

New bounds for roots of polynomials based on Fiedler companion matrices∗

Several matrix norms of the classical Frobenius companion matrices of a monic polynomial p(z) have been used in the literature to obtain simple lower and upper bounds on the absolute values of the roots λ of p(z). Recently, M. Fiedler has introduced a new family of companion matrices of p(z) (Lin. Alg. Appl., 372 (2003) 325-331) that has received considerable attention and it is natural to inve...