Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations

Petr Tichý; Jan Zítko

Displaying similar documents to “Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations”

A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space

L.O. Jolaoso, H.A. Abass, O.T. Mewomo (2019)

Archivum Mathematicum

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In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of $δ$ -demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition $\sum_{n = 1}^{\infty} β_{n} ∥ x_{n - 1} - x_{n} ∥ < + \infty$ on the inertial term. Finally,...

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...

On the weighted Euclidean matching problem in $ℝ^{d}$

Birgit Anthes, Ludger Rüschendorf (2001)

Applicationes Mathematicae

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A partitioning algorithm for the Euclidean matching problem in $ℝ^{d}$ is introduced and analyzed in a probabilistic model. The algorithm uses elements from the fixed dissection algorithm of Karp and Steele (1985) and the Zig-Zag algorithm of Halton and Terada (1982) for the traveling salesman problem. The algorithm runs in expected time $n {(l o g n)}^{p - 1}$ and approximates the optimal matching in the probabilistic sense.

A descent algorithm for $ε$ - approximation of continuous functions with values in unitary space

M. Janc (1982)

Matematički Vesnik

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An interior-point algorithm for semidefinite least-squares problems

Chafia Daili, Mohamed Achache (2022)

Applications of Mathematics

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We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the algorithm uses only full Nesterov-Todd steps with the advantage that no line search is required. Under new appropriate choices of the parameter $β$ which defines the size of the neighborhood of the central-path and of the parameter $θ$ which determines the rate of decrease of the barrier parameter, we show that the proposed algorithm is well defined...

A stochastic mirror-descent algorithm for solving $A X B = C$ over an multi-agent system

Yinghui Wang, Songsong Cheng (2021)

Kybernetika

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In this paper, we consider a distributed stochastic computation of $A X B = C$ with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of $A X B = C$ , we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm....

Distributed accelerated Nash equilibrium learning for two-subnetwork zero-sum game with bilinear coupling

Xianlin Zeng, Lihua Dou, Jinqiang Cui (2023)

Kybernetika

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This paper proposes a distributed accelerated first-order continuous-time algorithm for $O (1 / t^{2})$ convergence to Nash equilibria in a class of two-subnetwork zero-sum games with bilinear couplings. First-order methods, which only use subgradients of functions, are frequently used in distributed/parallel algorithms for solving large-scale and big-data problems due to their simple structures. However, in the worst cases, first-order methods for two-subnetwork zero-sum games often have an asymptotic...

An improvement of Euclid's algorithm

Zítko, Jan, Kuřátko, Jan

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The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using $c$ - $s$ transformation and $Q R$ -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.