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CSDP, a C library for semidefinite programming.
, 1997
"... this paper is organized as follows. First, we discuss the formulation of the semidefinite programming problem used by CSDP. We then describe the predictor corrector algorithm used by CSDP to solve the SDP. We discuss the storage requirements of the algorithm as well as its computational complexity. ..."
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Cited by 144 (1 self)
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this paper is organized as follows. First, we discuss the formulation of the semidefinite programming problem used by CSDP. We then describe the predictor corrector algorithm used by CSDP to solve the SDP. We discuss the storage requirements of the algorithm as well as its computational complexity. Finally, we present results from the solution of a number of test problems. 2 The SDP Problem We consider semidefinite programming problems of the form max tr (CX)
Parallel ScaLAPACKstyle Algorithms for Solving ContinuousTime Sylvester Equations
 In EuroPar 2003 Parallel Processing, H. Kosch and et al, Eds. Lecture Notes in Computer Science
, 2003
"... Abstract. An implementation of a parallel ScaLAPACKstyle solver for the general Sylvester equation, op(A)X − Xop(B) = C, where op(A) denotes A or its transpose A T, is presented. The parallel algorithm is based on explicit blocking of the BartelsStewart method. An initial transformation of the co ..."
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Cited by 8 (7 self)
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Abstract. An implementation of a parallel ScaLAPACKstyle solver for the general Sylvester equation, op(A)X − Xop(B) = C, where op(A) denotes A or its transpose A T, is presented. The parallel algorithm is based on explicit blocking of the BartelsStewart method. An initial transformation of the coefficient matrices A and B to Schur form leads to a reduced triangular matrix equation. We use different matrix traversing strategies to handle the transposes in the problem to solve, leading to different new parallel wavefront algorithms. We also present a strategy to handle the problem when 2 x 2 diagonal blocks of the matrices in Schur form, corresponding to complex conjugate pairs of eigenvalues, are split between several blocks in the block partitioned matrices. Finally, the solution of the reduced matrix equation is transformed back to the originally coordinate system. The implementation acts in a ScaLAPACK environment using 2dimensional block cyclic mapping of the matrices onto a rectangular grid of processes. Real performance results are presented which verify that our parallel algorithms are reliable and scalable. Keywords: Sylvester matrix equation, continuoustime, Bartels–Stewart
A Web Computing Environment for the SLICOT Library
, 2001
"... A prototype web computing environment for computations related to the design and analysis of control systems using the SLICOT software library is presented. The web interface can be accessed from a standard world wide web browser with no need for additional software installations on the local machin ..."
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Cited by 5 (3 self)
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A prototype web computing environment for computations related to the design and analysis of control systems using the SLICOT software library is presented. The web interface can be accessed from a standard world wide web browser with no need for additional software installations on the local machine. The environment provides userfriendly access to SLICOT routines where runtime options are specified by mouse clicks on appropriate buttons. Input data can be entered directly into the web interface by the user or uploaded from a local computer in a standard text format or in Matlab binary format. Output data is presented in the web browser window and possible to download in a number of different formats, including Matlab binary. The environment is ideal for testing the SLICOT software before performing a software installation or for performing a limited number of computations. It is also highly recommended for education as it is easy to use, and basically selfexplanatory, with the users' guide integrated in the user interface.
Combining Explicit and Recursive Blocking for Solving Triangular SylvesterType Matrix Equations on Distributed Memory Platforms
 In M. Danelutto, D. Laforenza, M. Vanneschi (EDS.): EuroPar 2004, Lecture Notes in Computer Science
, 2004
"... Abstract. Parallel ScaLAPACKstyle hybrid algorithms for solving the triangular continuoustime Sylvester (SYCT) equation AX − XB = C using recursive blocked node solvers from the novel highperformance library RECSY are presented. We compare our new hybrid algorithms with parallel implementations b ..."
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Cited by 4 (2 self)
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Abstract. Parallel ScaLAPACKstyle hybrid algorithms for solving the triangular continuoustime Sylvester (SYCT) equation AX − XB = C using recursive blocked node solvers from the novel highperformance library RECSY are presented. We compare our new hybrid algorithms with parallel implementations based on the SYCT solver DTRSYL from LAPACK. Experiments show that the RECSY solvers can significantly improve on the serial as well as on the parallel performance if the problem data is partitioned and distributed in an appropriate way. Examples include cutting down the execution time by 47 % and 34 % when solving largescale problems using two different communication schemes in the parallel algorithm and distributing the matrices with blocking factors four times larger than normally. The recursive blocking is automatic for solving subsystems of the global explicit blocked algorithm on the nodes. Keywords: Sylvester matrix equation, continuoustime, Bartels–Stewart
Towards an Accurate Performance Modeling of Parallel Sparse
 LU Factorization, in "Applicable Algebra in Engineering, Communication, and Computing
, 2006
"... We present a simulationbased performance model to analyze a parallel sparse LU factorization algorithm on modern cachedbased, highend parallel architectures. We consider supernodal rightlooking parallel factorization on a bidimensional grid of processors, that uses static pivoting. Our model ch ..."
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Cited by 4 (1 self)
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We present a simulationbased performance model to analyze a parallel sparse LU factorization algorithm on modern cachedbased, highend parallel architectures. We consider supernodal rightlooking parallel factorization on a bidimensional grid of processors, that uses static pivoting. Our model characterizes the algorithmic behavior by taking into account the underlying processor speed, memory system performance, as well as the interconnect speed. The model is validated using the implementation in the SuperLU DIST linear system solver, the sparse matrices from real application, and an IBM POWER3 parallel machine. Our modeling methodology can be adapted to study performance of other types of sparse factorizations, such as Cholesky or QR, and on different parallel machines. 1
Parallel Triangular SylvesterType Matrix Equation Solvers for SMP Systems using Recursive Blocking
 in Applied Parallel Computing. New Paradigms for HPC in Industry and Academia
, 2000
"... We present recursive blocked algorithms for solving triangular Sylvestertype matrix equations. Recursion leads to automatic blocking that is variable and "squarish". The main part of the computations are performed as level 3 general matrix multiply and add (GEMM) operations. We also present new hig ..."
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Cited by 2 (1 self)
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We present recursive blocked algorithms for solving triangular Sylvestertype matrix equations. Recursion leads to automatic blocking that is variable and "squarish". The main part of the computations are performed as level 3 general matrix multiply and add (GEMM) operations. We also present new highly optimized superscalar kernels for solving smallsized matrix equations stored in level 1 cache. Hereby, a larger part of the total execution time will be spent in GEMM operations. In turn, this leads to much better performance, especially for small to mediumsized problems, and improved parallel scalability on shared memory processor (SMP) systems. Uniprocessor and SMP parallel performance results are presented and compared with results from existing LAPACK routines for solving this type of matrix equations.