Reduction of huge, sparse matrices over finite fields via created catastrophes.
Riccati-like flows and matrix approximations
Roundoff errors in the fast computation of discrete convolutions
The efficient evaluation of a discrete convolution is usually carried out as a repated evaluation of a discrete convolution of a special type with the help of the fast Fourier transform. The paper is concerned with the analysis of the roundoff errors in the fast computation of this convolution. To obtain a comparison, the roundoff errors in the usual (direct) computation of this convolution are also considered. A stochastic model of the propagation of roundoff errors. is employed. The theoretical...
Smith normal form of a matrix of generalized polynomials with rational exponents
It is proved that generalized polynomials with rational exponents over a commutative field form an elementary divisor ring; an algorithm for computing the Smith normal form is derived and implemented.
Smooth factorizations of matrix valued functions and their derivatives.
Solution of a system of linear equations with given error sets for coefficients
In the paper, a method is given for finding all solutions of a system of linear equations with interval coefficients and with additional supposition that these coefficients fulfil a given system of homogeneous linear equations.
Sparse Null Basis Computations in Structural Optimization.
Stability and sensivity of Darboux transformation without parameter.
Stability of Fast Algorithms for Matrix Multiplication.
Statistical applications for equivariant matrices.
Stochastic Arithmetic Theory and Experiments
Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing...
Strong rank revealing Cholesky factorization.
Structure preserving algorithms for perplectic eigenproblems.
Structured conditioning of matrix functions.
Structured tools for structured matrices.
Symmetric matrix polynomial equations
The anti-symmetric ortho-symmetric solutions of the matrix equation XA=D.
The Chebyshev Solution of Certain Matrix Equations.
The Chebyshev Solution of the Linear Matrix Equation AX + YB = C.
The Coordinex Problem and Its Relation to the Conjecture of Wilkinson.