Computational Methods for General Sparse Matrices

Zlatev, Zahari

doi:10.1007/978-94-017-1116-6

Cited by 85 publications

(66 citation statements)

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“…While structural predictions of fill-in could be used in principle to set up static working data structures as in the case of Cholesky factorization, these predictions are often too pessimistic to be useful. Therefore, Z is stored by columns using dynamic data structures, similar to standard right-looking implementations of sparse unsymmetric Gaussian elimination; see, e.g., [39,83]. Nonzero entries of each column are stored consecutively as a segment of a larger workspace.…”

Section: Implementation Of Factorized Approximate Inversesmentioning

confidence: 99%

“…For larger problems, most operations are scattered around the memory and are out-of-cache. As a consequence, it is difficult to achieve high efficiency with the code, and any attempt to parallelize the computation of the preconditioner in this form will face serious problems (see [83] for similar comments in the context of sparse unsymmetric Gaussian elimination).…”

Section: Further Notes On Implementationsmentioning

confidence: 99%

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A comparative study of sparse approximate inverse preconditioners

Benzi

Tůma

1999

Applied Numerical Mathematics

224

200

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A number of recently proposed preconditioning techniques based on sparse approximate inverses are considered. A description of the preconditioners is given, and the results of an experimental comparison performed on one processor of a Cray C98 vector computer using sparse matrices from a variety of applications are presented. A comparison with more standard preconditioning techniques, such as incomplete factorizations, is also included. Robustness, convergence rates, and implementation issues are discussed.

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Section: Implementation Of Factorized Approximate Inversesmentioning

confidence: 99%

Section: Further Notes On Implementationsmentioning

confidence: 99%

A comparative study of sparse approximate inverse preconditioners

Benzi

Tůma

1999

Applied Numerical Mathematics

224

200

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“…This can cause difficulties, because the number of non-zeros per row is in general changed in the Step 3. Therefore some operations (moving rows to the end of the sparse arrays and even performing occasionally garbage collections; [5]) that are traditionally used in sparse techniques for general matrices must be carried in Step 4. This extra work can be reduced by (i) dropping small elements and (ii) avoiding the storage of Q i .…”

Section: Gathering the Non-zeros In One-dimensional Arraysmentioning

confidence: 99%

“…C is never formed explicitly; one works the whole time with A and R. Q, which is normally rather dense, is neither stored nor used in the iterative process (see [5]). …”

Section: Gathering the Non-zeros In One-dimensional Arraysmentioning

confidence: 99%

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Using dense matrix computations in the solution of sparse problems

Ostromsky

Zlatev

1997

Lecture Notes in Computer Science

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Abstract. On many high-speed computers the dense matrix technique is preferable to sparse matrix technique when the matrices are not very large, because the high computational speed compensates fully the disadvantages of using more arithmetic operations and more storage. Dense matrix techniques can still be used if the computations are successively carried out in a sequence of large dense blocks. A method based on this idea will be discussed. Statement of the problemConsider: Ax = b − r with A T r = 0, where A ∈ R m×n , m ≥ n, rank(A) = n, b ∈ R m×1 , r ∈ R m×1 and x ∈ R n×1 . It is difficult to use efficiently highspeed computers for solving the above problem if matrix A is general sparse. For dense matrices all difficulties disappear and the speed of the dense matrix computations is normally close to the peak performance of the computer used; see Table 1. A new method will be described. The method is based on a reordering algorithm LORA, [3], [4], which allows us to form easily a sequence of relatively large blocks. The blocks are handled as dense matrices. This is a trade off procedure: it is accepted to perform more computations, but with higher

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Large‐Scale Algebraic Equations

2023

Graph Database and Graph Computing for Power System Analysis

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Computational Methods for General Sparse Matrices

Abstract: Zlatev, Zahari, 1939-Computational methods for general sparse matrices I by Zahari Zlatev.p. em. -- Inc 1 udes index.

Cited by 85 publications

References 0 publications

A comparative study of sparse approximate inverse preconditioners

A comparative study of sparse approximate inverse preconditioners

Using dense matrix computations in the solution of sparse problems

Large‐Scale Algebraic Equations

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