Results 201 to 210 of about 30,039 (240)
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2018
In Chap. 4 we learned how to diagonalize a square matrix using the Eigen decomposition. Eigen decomposition has many uses, but it has a limitation: it can only be applied to a square matrix. In this chapter, we will learn how to extend the decomposition to a rectangular matrix using a related method known as a Singular Value Decomposition (SVD ...
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In Chap. 4 we learned how to diagonalize a square matrix using the Eigen decomposition. Eigen decomposition has many uses, but it has a limitation: it can only be applied to a square matrix. In this chapter, we will learn how to extend the decomposition to a rectangular matrix using a related method known as a Singular Value Decomposition (SVD ...
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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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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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Randomized Generalized Singular Value Decomposition
Communications on Applied Mathematics and Computation, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wei, Wei +3 more
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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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2010
In many modern applications involving large data sets, statisticians are confronted with a large m×n matrix X = (x ij) that encodes n features on each of mobjects. For instance, in gene microarray studies x ij represents the expression level of the ith gene under the jth experimental condition [13].
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In many modern applications involving large data sets, statisticians are confronted with a large m×n matrix X = (x ij) that encodes n features on each of mobjects. For instance, in gene microarray studies x ij represents the expression level of the ith gene under the jth experimental condition [13].
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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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Downdating the Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications, 1995Let \(A\) be a matrix with known singular values and left and/or right singular vectors, and let \(A'\) be the matrix obtained by deleting a row from \(A\). Computing the singular value decomposition (SVD) of \(A'\) from the SVD of \(A\) is called the downdating singular value decomposition problem (DSVDP).
Gu, Ming, Eisenstat, Stanley C.
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Continuation of Singular Value Decompositions
Mediterranean Journal of Mathematics, 2005In this work we consider computing a smooth path for a (block) singular value decomposition of a full rank matrix valued function. We give new theoretical results and then introduce and implement several algorithms to compute a smooth path. We illustrate performance of the algorithms with a few numerical examples.
L. DIECI L +2 more
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