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The hyperbolic singular value decomposition and applications
Proceedings of the 32nd Midwest Symposium on Circuits and Systems, 1990A new generalization of singular value decomposition (SVD), the hyperbolic SVD, is advanced, and its existence is established under mild restrictions. Two algorithms for effecting this decomposition are discussed. The new decomposition has applications in downdating in problems where the solution depends on the eigenstructure of the normal equations ...
Ruth Onn +2 more
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Generalizing the Singular Value Decomposition
SIAM Journal on Numerical Analysis, 1976Two generalizations of the singular value decomposition are given. These generalizations provided a unified way of regarding certain matrix problems and the numerical techniques which are used to s...
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The QLP Approximation to the Singular Value Decomposition
SIAM Journal on Scientific Computing, 1999A new decomposition, termed the pivoted QLP-decomposition, of a matrix is introduced. It is a postprocessing step to the pivoted QR-decomposition, used to determine the rank of a matrix. It is simply a further pivoted QR-decomposition of \(R^T\) of the first decomposition.
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Functional Tensor Singular Value Decomposition
SIAM Journal on Scientific ComputingzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chuan Wang 0001 +4 more
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1994
Many numerical methods used in application areas such as signal processing, estimation, and control are based on the singular value decomposition (SVD) of matrices. The SVD is widely used in least squares estimation, systems approximations, and numerical linear algebra.
Uwe Helmke, John B. Moore
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Many numerical methods used in application areas such as signal processing, estimation, and control are based on the singular value decomposition (SVD) of matrices. The SVD is widely used in least squares estimation, systems approximations, and numerical linear algebra.
Uwe Helmke, John B. Moore
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The Singular Value Decomposition
2015The matrix decomposition introduced in this chapter is very important in many practical applications, since it yields the best possible approximation (in a certain sense) of a given matrix by a matrix of low rank. A low rank approximation can be considered a “compression” of the data represented by the given matrix.
Jörg Liesen, Volker Mehrmann
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Nonlinear singular value decomposition
2017Linear functions are widely used and well-understood. For example, to solve f(x) = 0 or f(x) = λx, with linear f, we can rely on matrix decompositions (singular value decomposition (SVD), eigenvalue decomposition (EVD), etc.). On the other hand, having nonlinear multivariate vector functions (multiple input-multiple output static nonlinearities), it is
Ishteva, Mariya Kamenova +1 more
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1993
In this chapter we discuss reduction of matrices to the canonical form by use of orthogonal transformations in the spaces of images and preimages. Such canonical form is called the singular value decomposition. In what follows we will use the well-known polar decomposition, which is recalled in Section 1 in course of discussion of singular value ...
S. K. Godunov +3 more
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In this chapter we discuss reduction of matrices to the canonical form by use of orthogonal transformations in the spaces of images and preimages. Such canonical form is called the singular value decomposition. In what follows we will use the well-known polar decomposition, which is recalled in Section 1 in course of discussion of singular value ...
S. K. Godunov +3 more
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The Singular Value Decomposition
2020The factorization is easily verified. Here \( \mathit\mathbf{U}=\mathit\mathbf{V}=\frac{1}{\sqrt{2}} \left[ \begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array} \right], \)which is clearly unitary. Since in addition the matrix in the middle is diagonal, it follows that this is both a spectral and a singular value decomposition.
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2020
In Chapter 3, we learned that certain types of matrices, which are referred to as positive semidefinite matrices, can be expressed in the following form: $$\displaystyle A= V \varDelta V^T $$ Here, V is a d × d matrix with orthonormal columns, and Δ is a d × d diagonal matrix with nonnegative eigenvalues of A. The orthogonal matrix V can also be
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In Chapter 3, we learned that certain types of matrices, which are referred to as positive semidefinite matrices, can be expressed in the following form: $$\displaystyle A= V \varDelta V^T $$ Here, V is a d × d matrix with orthonormal columns, and Δ is a d × d diagonal matrix with nonnegative eigenvalues of A. The orthogonal matrix V can also be
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