A Stable Parallel Algorithm for Diagonally Dominant Tridiagonal Linear Systems

Rao, S. Chandra Sekhara; Kamra, Rabia

doi:10.1109/hipc.2015.31

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…In addition, the present factorization has the property that vector [ a ,0,…,0, b ] T is invariant under the transformation W . With this property, tridiagonal parallel solvers were constructed. However, the W Z factorizations given earlier do not have this vector invariant property.…”

Section: Introductionmentioning

confidence: 99%

“…Due to this, while computing the solution of the subsystem Zx = y, where Wy = f, we need to solve a 2 × 2 lower triangular system at each stage, rather than 2 × 2 dense systems. 12 In addition, the present factorization has the property that vector [a, 0, … , 0, b] T is invariant under the transformation W. With this property, tridiagonal parallel solvers 16,17 were constructed. However, the WZ factorizations given earlier 12,14,18,19 do not have this vector invariant property.…”

Section: Introductionmentioning

confidence: 99%

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A hybrid parallel algorithm for large sparse linear systems

Rao

Kamra

2018

Numerical Linear Algebra App

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Summary Large sparse linear systems arise in many areas of scientific computing, and the solution of these systems is the most time‐consuming part in many large‐scale problems. We present a hybrid parallel algorithm, named incomplete WZ parallel solver (IWZPS), for the solution of large sparse nonsingular diagonally dominant linear systems on distributed memory architectures. The method is a combination of both direct and iterative techniques. We compare the present hybrid parallel sparse algorithm IWZPS with the direct and iterative sparse solvers, namely, MUMPS and ILUPACK, respectively. In addition, we compare it with a hybrid parallel solver, DDPS.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A hybrid parallel algorithm for large sparse linear systems

Rao

Kamra

2018

Numerical Linear Algebra App

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“…Theorem 3.4. [21]. Let B be nonsingular tri-diagonal diagonally dominant, then its factored Z-matrix from QIF factorization is also tri-diagonal diagonally dominant.…”

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confidence: 99%

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

Bashir

Kamarulhaili

Babarinsa

2023

J. Nig. Soc. Phys. Sci.

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Quadrant Interlocking Factorization (QIF), an alternative to LU factorization, is suitable for factorizing invertible matrix A such that det(A) , 0. The QIF, with its application in parallel computing, is the most efficient matrix factorization technique yet underutilized. The two forms of QIF among others, which are not only similar in algorithm but also in computation, are WZ factorization and WH factorization yet differs in applications and properties. This review discusses both the old form of QIF, called WZ factorization, and the latest form of QIF, called WH factorization, with an example and open questions to further the studies between the two factorization techniques.

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A stable parallel algorithm for block tridiagonal toeplitz–block–toeplitz linear systems

Kamra

Rao

2021

Mathematics and Computers in Simulation

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A Stable Parallel Algorithm for Diagonally Dominant Tridiagonal Linear Systems

Cited by 4 publications

References 20 publications

A hybrid parallel algorithm for large sparse linear systems

A hybrid parallel algorithm for large sparse linear systems

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

A stable parallel algorithm for block tridiagonal toeplitz–block–toeplitz linear systems

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