Results 221 to 230 of about 1,484,501 (262)
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Constructive Approximation, 2004
This paper extends to a matrix setting many classical results from the scalar theory of orthogonal polynomials and Christoffel functions. Namely, the authors consider an \(N\times N\) matrix weight \(W\) (that is, a positive definite matrix of measures supported on \(\mathbb R\)), for which they define the sequence of matrix-valued orthonormal ...
Durán, Antonio J., Polo, Beatriz
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This paper extends to a matrix setting many classical results from the scalar theory of orthogonal polynomials and Christoffel functions. Namely, the authors consider an \(N\times N\) matrix weight \(W\) (that is, a positive definite matrix of measures supported on \(\mathbb R\)), for which they define the sequence of matrix-valued orthonormal ...
Durán, Antonio J., Polo, Beatriz
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Deflated Restarting for Matrix Functions
SIAM Journal on Matrix Analysis and Applications, 2011We investigate an acceleration technique for restarted Krylov subspace methods for computing the action of a function of a large sparse matrix on a vector. Its effect is to ultimately deflate a specific invariant subspace of the matrix which most impedes the convergence of the restarted approximation process.
Michael Eiermann +2 more
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A novel Beta matrix function via Wiman matrix function and their applications
Analysis, 2023Abstract Many authors defined and extended the beta function in various forms because the beta function has wide uses in different fields of science and applied science. In this article, we define a new more generalized form of the extended beta matrix function via the Wiman matrix function and describe their significant properties and ...
Nabiullah Khan, Saddam Husain
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Semismooth Matrix-Valued Functions
Mathematics of Operations Research, 2002Matrix-valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher's theorem ...
Defeng Sun, Jie Sun 0001
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Quaestiones Mathematicae, 2019
We introduce the generalized zeta matrix function, digamma matrix function and polygamma matrix function. We obtain the regions of convergence of these matrix functions, some recurrence relations and their integral representations. An identity involving hypergeometric matrix function 3F2 in the form of digamma matrix function is also given.Mathematics ...
Ravi Dwivedi, Vivek Sahai
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We introduce the generalized zeta matrix function, digamma matrix function and polygamma matrix function. We obtain the regions of convergence of these matrix functions, some recurrence relations and their integral representations. An identity involving hypergeometric matrix function 3F2 in the form of digamma matrix function is also given.Mathematics ...
Ravi Dwivedi, Vivek Sahai
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Matrix Functions and Matrix Equations
2015Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed.
Zhaojun Bai, Weiguo Gao, Yangfeng Su
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Improving of CE With the Matrix of Functions and Functionalities
2012The article discusses the theoretical and practical aspects of the factors influencing the concurrent development of a new product designed within an early development-and-construction process. Taking into account the previous methods like morphological matrices, a new method—the matrix of functions and functionalities (MFF)—has been identified and ...
Ziga Zadnik, Joze Duhovnik
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Approximation of Matrix-Valued Functions
SIAM Journal on Matrix Analysis and Applications, 1993Summary: It is shown that if \(f(z)=\sum^ \infty_{i=0} a_ i z^ i\) (the series having radius of convergence \(R\)) then for any \(n\times n\) matrix \(A\) with spectral radius less than \(R\) and any norm \(\|\cdot\|\) on the space of \(n\times n\) matrices \[ \left\| f(A)-\sum^ k_{i=0} a_ i A^ i\right\|\leq {1\over (k+1)!} \max_{s\in [0,1]}\| A^{k+1 ...
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More on Concavity of a Matrix Function
SIAM Journal on Matrix Analysis and Applications, 1998This paper generalizes a well-known result in statistical literature. The mapping \(A\mapsto (K'A^+K)^+\) is shown to be matrix concave and isotone when \(A\) varies over the set of symmetric nonnegative definite matrices whose range is invariant with respect to \(KK'\). In this paper, Section 2 contains the results and Section 3 is an application.
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The Boundary Matrix of Threshold Functions
IEEE Transactions on Electronic Computers, 1965In the design of registers for controlling a digital process, it is often desired to count through a sequence of specified length and terminate the count by returning to the initial state. A penalty is associated with the use of a straightforward binary code for such counters because of the large number of diodes required to implement the counter, and ...
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