Displaying similar documents to “Solution of transient problems of thermoelasticity”

Using successive approximations for improving the convergence of GMRES method

Jan Zítko (1998)

Applications of Mathematics

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In this paper, our attention is concentrated on the GMRES method for the solution of the system ( I - T ) x = b of linear algebraic equations with a nonsymmetric matrix. We perform m pre-iterations y l + 1 = T y l + b before starting GMRES and put y m for the initial approximation in GMRES. We derive an upper estimate for the norm of the error vector in dependence on the m th powers of eigenvalues of the matrix T . Further we study under what eigenvalues lay-out this upper estimate is the best one. The estimate shows and...

Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X -1 A=L

Maria Adam, Nicholas Assimakis (2015)

Open Mathematics

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In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic Riccati equation. The first algorithm requires the nonsingularity of the transition matrix and is based on the solution of a standard eigenvalue problem for a new symplectic matrix; the proposed algorithm computes the extreme solutions of the discrete algebraic Riccati equation. The second algorithm solves the Riccati equation without the assumption of the nonsingularity of the transition...

A note on the matrix Haffian.

Heinz Neudecker (2000)

Qüestiió

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This note contains a transparent presentation of the matrix Haffian. A basic theorem links this matrix and the differential ofthe matrix function under investigation, viz ∇F(X) and dF(X). Frequent use is being made of matrix derivatives as developed by Magnus and Neudecker.

Inversion of square matrices in processors with limited calculation abillities

Krzysztof Janiszowski (2003)

International Journal of Applied Mathematics and Computer Science

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An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced...