Fast QR Decomposition of Vandermonde-Like Mmatrices and Polynomial Least Squares Approximation
Copyright policy )Fast QR Decomposition of Vandermonde-Like Mmatrices and Polynomial Least Squares Approximation
Orthogonal polynomials with respect to a discrete inner product are computed via an inverse eigenvalue problem that is actually solved via Givens rotations. The algorithm is applied to factor Vandermonde-like matrices as \(QR\) and it provides a fast solver for overdetermined systems with such matrices.
\(QR\) factorization, overdetermined systems, Numerical solutions to overdetermined systems, pseudoinverses, algorithm, Vandermonde matrix, Algorithms for approximation of functions, discrete inner product, inverse eigenvalue problem, Givens rotations, Direct numerical methods for linear systems and matrix inversion, orthogonal polynomials, Orthogonalization in numerical linear algebra
\(QR\) factorization, overdetermined systems, Numerical solutions to overdetermined systems, pseudoinverses, algorithm, Vandermonde matrix, Algorithms for approximation of functions, discrete inner product, inverse eigenvalue problem, Givens rotations, Direct numerical methods for linear systems and matrix inversion, orthogonal polynomials, Orthogonalization in numerical linear algebra
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