Marco D’Apuzzo

In this paper we present a parallel iterative solver for large and sparse nonsymmetric linear systems. The solver is based on a row-projection algorithm, derived from the symmetrized block version of the Kaczmarz method with Conjugate Gradient acceleration. A comparison with some Krylov subspace methods shows the remarkable robustness of this algorithm when applied to systems with eigenvalues arbitrarily distributed in the complex plane. The parallel version of the algorithm was developed for MIMD distributed memory machines and it is based on a row partitioning approach which allows to compute each iteration as a simultaneous set of independent least squares problems. Moreover, we propose a data distribution strategy leading to a scalable communication scheme. The algorithm has been tested both on a system Intel iPSC/860 and on the Intel Touchstone DELTA System, running the Intel NX message passing environment.< >

Solver

MIMD

Distributed memory

Krylov subspace

Robustness

10.1109/empdp.1995.389178

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Citations (2)

On the iterative solution of KKT systems in potential reduction software for large-scale quadratic problems

Computational Optimization and Applications (2007)

Sonia Cafieri Marco D’Apuzzo Valentina De Simone Daniela di Serafino

Karush–Kuhn–Tucker conditions

Interior point method

10.1007/s10589-007-9035-y

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Citations (31)

Nonlinear Optimization: A Parallel Linear Algebra Standpoint

Marco D’Apuzzo Marina Marino Athanasios Migdalas Pãnos M. Pardalos Gerardo Toraldo

Linear algebra

10.1201/9781420028683-14

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Citations (0)

Modifying the Cholesky Factorization on MIMD Distributed Memory Machines

Applied optimization (1998)

Marco D’Apuzzo Valentina De Simone Marina Marino Gerardo Toraldo

MIMD

Kernel (algebra)

Distributed memory

Minimum degree algorithm

10.1007/978-1-4613-3279-4_9

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Citations (1)

Scalability and load balancing in adaptive algorithms for multidimensional integration

Parallel Computing (1997)

Marco D’Apuzzo Marco Lapegna A. Murli

MIMD

Distributed memory

10.1016/s0167-8191(97)00017-3

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Citations (17)

A parallel block row‐action method for solving large sparse linear systems on distributed memory multiprocessors

Concurrency Practice and Experience (1994)

Marco D’Apuzzo Maria Assunta De Rosa

Abstract Recently developed block‐iterative versions of some row‐action algorithms for solving general systems of sparse linear equations allow parallelism in the computations when the underlying problem is appropriately decomposed. However, problems associated with the parallel implementation of these algorithms have to be addressed. In this paper we present an implementation on distributed memory multiprocessors of a block version of the Kaczmarz row‐action method. One of the main issues related to the efficient implementation of this method on a concurrent environment is to develop suitable communication schemes in order to reduce the amount of communication needed at each iteration. We propose two data distribution strategies which lead to different computation and communication schemes. To verify and compare the effectiveness of the proposed strategies, numerical experiments have been carried out on a Symult S2010 and a Meiko Computing Surface. The performance evaluation has been done using a scaled efficiency model.

Distributed memory

10.1002/cpe.4330060105

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Citations (1)

ON THE USE OF AN APPROXIMATE CONSTRAINT PRECONDITIONER IN A POTENTIAL REDUCTION ALGORITHM FOR QUADRATIC PROGRAMMING

Sonia Cafieri Marco D’Apuzzo Valentina De Simone Daniela di Serafino

10.1142/9789812709394_0020

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Citations (3)

Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints

Journal of Optimization Theory and Applications (2006)

Sonia Cafieri Marco D’Apuzzo Marina Marino Antonio Mucherino Gerardo Toraldo