grotto
发表于 2025-3-25 06:17:20
Solution of Symmetric and Unsymmetric Band Equations and the Calculations of Eigenvectors of Band MaIn an earlier paper in this series the triangular factorization of positive definite band matrices was discussed. With such matrices there is no need for pivoting, but with non-positive definite or unsymmetric matrices pivoting is necessary in general, otherwise severe numerical instability may result even when the matrix is well-conditioned.
PALMY
发表于 2025-3-25 11:31:26
Solution of Real and Complex Systems of Linear EquationsIf . is a non-singular matrix then, in general, it can be factorized in the form . = ., where . is lower-triangular and . is upper-triangular. The factorization, when it exists, is unique to within a non-singular diagonal multiplying factor.
手势
发表于 2025-3-25 13:48:13
Linear Least Squares Solutions by Housholder TransformationsLet . be a given .×. real matrix with .≧. and of rank . and . a given vector. We wish to determine a vector . such that.where ∥ … ∥ indicates the euclidean norm. Since the euclidean norm is unitarily invariant.where .=.. and ... = .. We choose . so that.and . is an upper triangular matrix. Clearly,.where . denotes the first . components of ..
tolerance
发表于 2025-3-25 19:21:28
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cochlea
发表于 2025-3-25 23:32:15
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善辩
发表于 2025-3-26 00:49:09
The Jacobi Method for Real Symmetric MatricesAs is well known, a real symmetric matrix can be transformed iteratively into diagonal form through a sequence of appropriately chosen . (in the following called .):.where ..= ..(.) is an orthogonal matrix which deviates from the unit matrix only in the elements
Malfunction
发表于 2025-3-26 05:54:20
The Implicit , AlgorithmIn an algorithm was described for carrying out the . algorithm for a real symmetric matrix using shifts of origin. This algorithm is described by the relations.where .. is orthogonal, .. is lower triangular and .. is the shift of origin determined from the leading 2×2 matrix of ...
Myofibrils
发表于 2025-3-26 10:59:41
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Abduct
发表于 2025-3-26 13:48:07
978-3-642-86942-6Springer-Verlag Berlin Heidelberg 1971
克制
发表于 2025-3-26 17:22:16
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