Titlebook: Handbook for Automatic Computation; Volume II: Linear Al J. H. Wilkinson,C. Reinsch,F. L. Bauer,A. S. House Book 1971 Springer-Verlag Berli

Dignant

https://doi.org/10.1007/978-94-007-6683-9as based on the Cholesky factorization of .. If A is ill-conditioned the computed solution may not be sufficiently accurate, but (provided A is not almost singular to working accuracy) it may be improved by an iterative procedure in which the Cholesky decomposition is used repeatedly.

散步

Arb853

https://doi.org/10.1007/978-3-319-55509-6 . largest eigenvalues of .., and the matrix . consists of the orthonormalized eigenvectors of .... The diagonal elements of . are the non-negative square roots of the eigenvalues of ...; they are called .. We shall assume that.Thus if .=., σ. = σ.=⋯=σ. = 0. The decomposition (1) is called the . (SV

啜泣

使痛苦

https://doi.org/10.1007/978-3-319-92796-1 unitary and . is upper-triangular then.that is, . is unitarily similar to .. By repeated application of the above result a sequence of matrices which are unitarily similar to a given matrix .. may be derived from the relations.and, in general, .. tends to upper-triangular form.

变化

https://doi.org/10.1007/978-1-4684-1713-5corput rections in combination with . steps. If an initial shift has rendered the matrix positive or negative definite, then this property is preserved throughout the iteration. Thus, the . step may be achieved by two successive Cholesky . steps or equivalently, since the matrix is tridiagonal, by t

壮丽的去

Iterative Refinement of the Solution of a Positive Definite System of Equationsas based on the Cholesky factorization of .. If A is ill-conditioned the computed solution may not be sufficiently accurate, but (provided A is not almost singular to working accuracy) it may be improved by an iterative procedure in which the Cholesky decomposition is used repeatedly.

丧失

浪费物质

Singular Value Decomposition and Least Squares Solutions . largest eigenvalues of .., and the matrix . consists of the orthonormalized eigenvectors of .... The diagonal elements of . are the non-negative square roots of the eigenvalues of ...; they are called .. We shall assume that.Thus if .=., σ. = σ.=⋯=σ. = 0. The decomposition (1) is called the . (SV

Bravura

Householder’s Tridiagonalization of a Symmetric Matrixd since its publication and in view of its importance it seems worthwhile to issue improved versions of the procedure given there. More than one variant is given since the most efficient form of the procedure depends on the method used to solve the eigenproblem of the derived tridiagonal matrix.