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SIAM Journal on Control and Optimization, 2009
We give a necessary and sufficient condition for the existence of a matrix $F$ such that the singular values of $A+BF$ are the prescribed values. We also give a simple algorithm to compute $F$ if the prescribed values satisfy the condition.
Clyde F. Martin, Xiaochang A. Wang
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We give a necessary and sufficient condition for the existence of a matrix $F$ such that the singular values of $A+BF$ are the prescribed values. We also give a simple algorithm to compute $F$ if the prescribed values satisfy the condition.
Clyde F. Martin, Xiaochang A. Wang
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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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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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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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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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2002
3.1 Matrix Young Inequalities 3.2 Singular Values of Hadamard Products 3.3 Differences of Positive Semidefinite Matrices 3.4 Matrix Cartesian Decompositions 3.5 Singular Values and Matrix ...
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3.1 Matrix Young Inequalities 3.2 Singular Values of Hadamard Products 3.3 Differences of Positive Semidefinite Matrices 3.4 Matrix Cartesian Decompositions 3.5 Singular Values and Matrix ...
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