Decay bounds and algorithms for approximating functions of sparse matrices.
Decomposition of a Symmetric Matrix (Handbook Series Linear Algebra).
Decomposition of an updated correlation matrix via hyperbolic transformations
An algorithm for hyperbolic singular value decomposition of a given complex matrix based on hyperbolic Householder and Givens transformation matrices is described in detail. The main application of this algorithm is the decomposition of an updated correlation matrix.
Decompositional analysis of Kronecker structured Markov chains.
Degeneration and complexity of bilinear maps: Some asymptotic spectra.
Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations
Lanczos’ method for solving the system of linear algebraic equations consists in constructing a sequence of vectors in such a way that and . This sequence of vectors can be computed by the BiCG (BiOMin) algorithm. In this paper is shown how to obtain the recurrences of BiCG (BiOMin) directly from this conditions.
Derivation of high-order spectral methods for time-dependent PDE using modified moments.
Determinant evaluations for binary circulant matrices
Determinant formulas for special binary circulant matrices are derived and a new open problem regarding the possible determinant values of these specific circulant matrices is stated. The ideas used for the proofs can be utilized to obtain more determinant formulas for other binary circulant matrices, too. The superiority of the proposed approach over the standard method for calculating the determinant of a general circulant matrix is demonstrated.
Determinants of Legendre symbol matrices
Determinants of multiplicative Toeplitz matrices
Determinatenabschätzung für binäre Matrizen mit n ... 3 mod 4.
Determination of matrices of the desired 2-D characteristic polynomial
Die Determinantenmethode zur Berechnung des charakteristischen Exponenten der endlichen Hillschen Differentialgleichung.
Differencial equations for the analytic singular value decomposition of a matrix.
Direct Error Analysis for Least Squares.
Direct iterative methods for linear systems using weak splittings
Direct methods for matrix Sylvester and Lyapunov equations.
Directed forests with application to algorithms related to Markov chains
This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.
Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems.
Discrete-time symmetric polynomial equations with complex coefficients
Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.