Results 271 to 280 of about 96,557 (302)
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Positivity of Block Tridiagonal Matrices
SIAM Journal on Matrix Analysis and Applications, 1998The authors give some results concerning the disconjugacy of linear Hamiltonian difference systems \[ \Delta x_k = A_k x_{k+1} + B_k u_k,\quad \Delta u_k = C_k x_{k+1} - A_k^T u_k \] and hence positive definiteness of the discrete quadratic functional \[ {\mathcal F}(x,u) ={\sum_{k=0}^N} \{u_k^T B_k u_k + x_{k+1}^T C_k x_{k+1}\} \] to positive ...
Martin Bohner, Ondrej Doslý
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A Block Generalization of Nekrasov Matrices
Journal of Mathematical Sciences, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1989
In the present paper the authors make an attempt to give a uniform description of the main properties of tridiagonal, band, block tridiagonal and block band matrices and their inverses. Some basic concepts are recalled and also some new results are presented.
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In the present paper the authors make an attempt to give a uniform description of the main properties of tridiagonal, band, block tridiagonal and block band matrices and their inverses. Some basic concepts are recalled and also some new results are presented.
ROSZA P +3 more
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Matrices Doubly Stochastic by Blocks
Canadian Journal of Mathematics, 1977The present work stems from the following classical result, due to G. H. Hardy, J. E. Littlewood, G. Pólya [7], and R. Rado [10].THEOREM 1. Concerning a pair of n-tuples x, y ϵ Rn, the following four statementsare equivalent:(a) for every continuous, convex function f : R ...
Fischer, Pal, Holbrook, John A. R.
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Symmetric Matrices with Alternating Blocks
1989A statement in algebraic geometry over fields of arbitrary characteristic follows from the existence of matrices with integer entries of the type mentioned in the title. It is shown how these matrices can be built from a finite number of small matrices. It is reported how these small matrices, of which the largest is a 25 by 25 matrix, were found using
Hefez, Abramo, Thorup, Anders
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A POLYNOMIAL PRECONDITIONER FOR BLOCK TRIDIAGONAL MATRICES
Parallel Algorithms and Applications, 1994ABSTRACT This paper is concerned with the solution of block tridiagonal linear systems by the preconditioned conjugate gradient (PCG) method. If we consider a block AGE splitting of the coefficient matrix, it is possible to derive an additive polynomial preconditioner and to give conditions for such preconditioner to be symmetric positive definite ...
GALLIGANI, Emanuele, V. RUGGIERO
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A Block Projection Method for Sparse Matrices
SIAM Journal on Scientific and Statistical Computing, 1992For the solution of systems of linear algebraic equations with sparse matrices the block Cimmino method is employed. Let the system be written as \[ \begin{pmatrix} A^ 1\\A^ 2\\\vdots\\ A^ p\end{pmatrix} x=\begin{pmatrix} b^ 1\\ b^ 2\\ \vdots \\b^ p\end{pmatrix} \] where the \(A^ i\) are matrices and the \(b^ i\) vectors.
Mario Arioli +3 more
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On the Index of Block Upper Triangular Matrices
SIAM Journal on Matrix Analysis and Applications, 1995This paper gives a precise characterization of the size of the largest Jordan block for the eigenvalue zero (called the index) of \(M = [\begin{smallmatrix} A & X \\ 0 & B \end{smallmatrix}]\) where \(A\) and \(B\) are both singular in terms of statements about the powers of \(M\) and their diagonal block images and kernels, the height and depth of ...
Rafael Bru +2 more
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A Note on Preconditioned Block Toeplitz Matrices
SIAM Journal on Scientific Computing, 1995\textit{T. Ku} and \textit{C. Kuo} [ibid. 13, No. 4, 948-966 (1992; Zbl 0756.65048)] proposed and analysed a block circulant preconditioner \(R_{mn}\) for solving a family of block Toeplitz systems \(T_{mn} x = b\). In the present paper, it is proved that the matrix \(T_{mn}\) is positive definite if the generating function \(f(x,y)\) of \(T_{mn}\) is ...
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1999
A Toeplitz matrix is constant along the parallels to the main diagonal. Matrices whose entries in the parallels to the main diagonal form periodic sequences (with the same period N) are referred to as block Toeplitz matrices. Equivalently, A is a block Toeplitz matrix if and only if $$ A = \left( {\begin{array}{*{20}{c}} {{a_0}}{{a_{ - 1}}}{{a_ ...
Albrecht Böttcher, Bernd Silbermann
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A Toeplitz matrix is constant along the parallels to the main diagonal. Matrices whose entries in the parallels to the main diagonal form periodic sequences (with the same period N) are referred to as block Toeplitz matrices. Equivalently, A is a block Toeplitz matrix if and only if $$ A = \left( {\begin{array}{*{20}{c}} {{a_0}}{{a_{ - 1}}}{{a_ ...
Albrecht Böttcher, Bernd Silbermann
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