Convergence of skew-symmetric iterative methods

Krukier, L. A.; Krukier, Boris L.

doi:10.3103/s1066369x11060090

Cited by 1 publication

(4 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The triangular skew-symmetric iterative methods [7] are defined in (1.2) with the matrix being chosen as…”

Section: Skew-symmetric Iterative Methodsmentioning

confidence: 99%

“…See [7]. Parameters α, β, γ are some values of the numerical ranges of the corresponding matrices given in (3.2).…”

Section: Convergence Of Skew-symmetric Iteration Methodsmentioning

confidence: 99%

“…See [7] for details. To investigate convergence of iterative methods we have to know eigen-property about matrix F , a product of the matrices A and B, which determinates the iterative method.…”

Section: Consider a System Of Linear Equationsmentioning

confidence: 99%

“…We will begin with short description of skew-symmetric iterative methods (SSM), then we will show that the field-of-values works for investigating the convergence of SSM, using formulas from [7], which connect fields-of-values of the matrices A, B, their symmetric part A 0 and skewsymmetric part A 1 , and eigenvalues of the iteration matrix G. These formulas will be used to derive sufficient conditions for convergence about matrix A when it is not positive real.…”

Section: It Is Known [4] That Sp(a) ⊆ H(a)mentioning

confidence: 99%

See 3 more Smart Citations

Using the Skew-Symmetric Iterative Methods for Solution of an Indefinite Nonsymmetric Linear Systems

Krukier¹

2014

JCM

View full text Add to dashboard Cite

The concept of the field of value to localize the spectrum of the iteration matrices of the skew-symmetric iterative methods is further exploited. Obtained formulas are derived to relate the fields of values of the original matrix and the iteration matrix. This allows us to determine theoretically that indefinite nonsymmetric linear systems can be solved by this class of iterative methods.Mathematics subject classification: 65F10.

show abstract

“…The triangular skew-symmetric iterative methods [7] are defined in (1.2) with the matrix being chosen as…”

Section: Skew-symmetric Iterative Methodsmentioning

confidence: 99%

“…See [7]. Parameters α, β, γ are some values of the numerical ranges of the corresponding matrices given in (3.2).…”

Section: Convergence Of Skew-symmetric Iteration Methodsmentioning

confidence: 99%

Section: Consider a System Of Linear Equationsmentioning

confidence: 99%

Section: It Is Known [4] That Sp(a) ⊆ H(a)mentioning

confidence: 99%

See 2 more Smart Citations