Maximally Orthogonal High-Order Basis Functions Have a Well-Conditioned Gram Matrix
نویسندگان
چکیده
منابع مشابه
Study on multi-order fractional differential equations via operational matrix of hybrid basis functions
In this paper we apply hybrid functions of general block-pulse functions and Legendre polynomials for solving linear and nonlinear multi-order fractional differential equations (FDEs). Our approach is based on incorporating operational matrices of FDEs with hybrid functions that reduces the FDEs problems to the solution of algebraic systems. Error estimate that verifies a converge...
متن کاملA Well-Conditioned Collocation Method Using a Pseudospectral Integration Matrix
In this paper, a well-conditioned collocation method is constructed for solving general p-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features: the condition number of the linear system is independent of the n...
متن کاملstudy on multi-order fractional differential equations via operational matrix of hybrid basis functions
in this paper we apply hybrid functions of general block-pulse functions and legendre polynomials for solving linear and nonlinear multi-order fractional differential equations (fdes). our approach is based on incorporating operational matrices of fdes with hybrid functions that reduces the fdes problems to the solution of algebraic systems. error estimate that verifies a converge...
متن کاملFast high-order algorithms and well-conditioned integral equations for high-frequency sound-hard scattering problems
This text introduces 1) New Regularized Combined Field Integral Equations (CFIE-R) for the solution of frequency-domain sound-hard scattering problems, and, 2) Fast, high-order algorithms for the numerical solution of the CFIE-R and related integral equations. Like the classical Combined Field Integral Equation (CFIE), the CFIE-R are unikely-solvable integral equations based on use of single an...
متن کاملImage Coding Using Orthogonal Basis Functions
The transform properties of several orthogonal basis functions are analysed in detail in this report, and their performance compared using a set of grayscale test images, containing both natural and artificial scenes. Well-defined image quality measures are used to determine the type of images that are most suitable for compression for a given basis function. The particular transforms that we h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Antennas and Propagation
سال: 2014
ISSN: 0018-926X,1558-2221
DOI: 10.1109/tap.2014.2323081