Block AOR Research Articles

Abstract 13533: Acute Post-operative Renal Failure and Mortality Risk Following Norwood Surgical Palliation: A Secondary Analysis of the Pediatric Heart Network Single Ventricle Reconstruction Trial Public Use Database

Introduction: The Single Ventricle Reconstruction (SVR) trial randomized neonates with a single morphologic right ventricle undergoing Norwood to a modified Blalock-Taussig shunt (mBTS) or a right ventricle-to-pulmonary artery shunt at 15 centers. The trial demonstrated increased risk of death or heart transplant at one-year post-Norwood in subjects randomized to a mBTS. Using SVR public data, we evaluated incidence and risk factors for post-op renal failure after Norwood, and evaluated the relationship between renal failure, shunt type and one-year post-Norwood mortality. Methods: Post-op renal failure was defined a-priori as a 3-fold rise in creatinine from baseline, or dialysis use within 7 days of Norwood. We used multivariate logistic regression to evaluate risk factors for post-op renal failure and Cox hazard regression to determine the association between post-op renal failure and one-year post-Norwood mortality. Results: Overall 46/544 (8.4%) SVR trial subjects developed post-op renal failure, the majority (32/46, 69.6%) by post-op day 3. In multivariate analysis, risk factors for post-op renal failure included receipt of a mBTS (aOR 3.3, p=0.02), center volume <15 cases/year (aOR 2.7, p=0.005), presence of ≥ 2 pre-op complications (aOR 4.0, p<0.001), low birth weight (aOR 3.2, p=0.002), post-op heart block (aOR 8.5, p=0.001), and delayed sternal closure (aOR 5.3, p=0.026). Renal failure was an independent risk factor for one-year post-Norwood mortality (aHR 1.9, CI 1.1-3.2, p=0.019). When renal failure and shunt type were included as model covariates, there was interaction (p=0.049) with renal failure attenuating the mortality risk associated with receipt of a mBTS (p=0.24), Figure. Conclusions: In the SVR trial, post-op renal failure was relatively common but with modifiable risk factors including receipt of a mBTS. Our findings suggest that post-op renal failure accounts for some of the increased mortality risk associated with the mBTS.

On parallel multisplitting block iterative methods for linear systems arising in the numerical solution of Euler equations

The paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of Euler equations. Some sufficient conditions for convergence are proposed. As special cases the convergence of the parallel block generalized AOR (BGAOR), the parallel block AOR (BAOR), the parallel block generalized SOR (BGSOR), the parallel block SOR (BSOR), the extrapolated parallel BAOR and the extrapolated parallel BSOR methods are presented. Furthermore, the convergence of the parallel block iterative methods for linear systems with special block tridiagonal matrices arising in the numerical solution of Euler equations are discussed. Finally, some examples are given to demonstrate the convergence results obtained in this paper.

On a class of multi-level preconditioners for Z-matrices

In this paper, we study the convergence of a class of multi-level preconditioners and corresponding block AOR iterative methods. Then, we give some comparison theorems for different preconditioning levels. Finally, the effectiveness of the proposed methods are shown by some numerical experiments.

The Block Aor Iterative Methods For Solving Fuzzy Linear Systems

In this article the block AOR Iterative methods are used for solving fuzzy linear systems. The convergence of the methods and functional relationship between eigenvalues in block AOR is investigated.

On product-type generalized block AOR method for augmented linear systems

The generalized inexact accelerated overrelaxation ( GIAOR) method was presented by Bai, Parlett and Wang (Numer. Math. 102(2005)1-38) for solving the augmented system of linear equations. In this paper, a product-type generalized block AOR ( PGBAOR ) method is proposed, which is a two-step generalization of the GIAOR method. Both convergence and semi-convergence of the PGBAOR method are proved for the nonsingular and the singular augmented linear systems.

Multi-level preconditioned block accelerated overrelaxation iteration method for z-matrices

A class of multi-level preconditioners and corresponding preconditioned block AOR iterative method are presented and studied in this paper. We analyze the convergence performance of the new method and give the comparison theorems for different preconditioning level. Numerical results further verify our theoretical analysis and show that the proposed method has faster convergence speed than existing preconditioned block AOR method.

Semiconvergence of P-regular splittings for solving singular linear systems

We investigate necessary and sufficient conditions for semiconvergence of a splitting for solving singular linear systems, where the coefficient matrix A is a singular EP matrix. When A is a singular Hermitian matrix, necessary and sufficient conditions for semiconvergence of P-regular splittings are given, which generalize known results. As applications, the necessary and sufficient conditions for semiconvergence of block AOR and SSOR iterative methods are derived. A numerical example is given to illustrate the theoretical results.

Convergence of block iterative methods for linear systems with generalized H-matrices

The paper studies the convergence of some block iterative methods for the solution of linear systems when the coefficient matrices are generalized H -matrices. A truth is found that the class of conjugate generalized H -matrices is a subclass of the class of generalized H -matrices and the convergence results of R. Nabben [R. Nabben, On a class of matrices which arises in the numerical solution of Euler equations, Numer. Math. 63 (1992) 411–431] are then extended to the class of generalized H -matrices. Furthermore, the convergence of the block AOR iterative method for linear systems with generalized H -matrices is established and some properties of special block tridiagonal matrices arising in the numerical solution of Euler equations are discussed. Finally, some examples are given to demonstrate the convergence results obtained in this paper.

Semiconvergence of block AOR method for singular p-cyclic matrices

In this paper, we discuss semiconvergence of the block AOR method for solving singular linear systems with p-cyclic matrices. Some sufficient conditions for the semiconvergence of the block AOR method for solving a general p-cyclic singular system are proved.

On parallel multisplitting iterative methods for singular linear systems

In this paper, the semiconvergence of parallel multisplitting iterative methods and extrapolated parallel methods for singular linear systems is discussed. Some sufficient conditions for semiconvergence are presented whenever the multisplittings are P-regular, sub-regular or nonnegative. As special cases the semiconvergence of parallel generalized AOR, block AOR, AOR, parallel generalized SOR, block SOR, SOR, extrapolated parallel (generalized, block) AOR and extrapolated parallel (generalized, block) SOR methods are proved.

Aor type iterative methods for solving least squares problems

In order to solve least squares problems, the block SOR, block SSOR and block AOR iterative methods are proposed and investigated by some authors. In this paper, we generalize the usual block AOR method. Other five AOR type iterative methods are defined. Then the convergence and divergence regions for the AOR methods are discussed.

Comparisons of Block Iterative Methods

Comparison theorems for spectral radii of two block USSOR methods, two block SSOR methods, two block AOR methods, two block SOR methods with respect to a partition π and the corresponding finer partition π* are given, respectively, whenever A is an M-matrix or an H-matrix.

Convergence of parallel multisplitting methods for h-matrices

This paper investigates the convergence of parallel multisplitting methods for solving linear systems Ax = b, where A is an H-matrix. Sufficient conditions of convergence for general parallel methods are derived. A class of parallel generalized AOR methods, parallel block AOR methods and parallel AOR methods are proposed, and many convergence conditions are obtained. In case A is an M-matrix, we compare the asymptotic convergence rates of the parallel methods.

Order-reducing conjugate gradients versus block AOR for constrained least-squares problems

We compare the convergence properties of two iterative algorithms for solving equality-constrained least-squares problems. The first algorithm, due to Barlow, Nichols, and Plemmons, applies a variation of the conjugate-gradient algorithm to a symmetric positive definite system which is smaller than the original problem. The second, block accelerated overrelaxation, is a two-parameter generalization of block SOR. Barlow, Nichols, and Plemmons have proven that their order-reducing conjugate-gradient algorithm converges faster than block SOR. We extend their result to show that the algorithm is also superior to block AOR. Numerical experiments on some structural engineering problems support the analysis.

Comparisons of nonnegative splittings of matrices

The comparison of the asymptotic rates of convergence of two iteration matrices induced by two splitting of the same matrix has arisen in the work of many authors. In this article, some new comparison theorems for two nonnegative splittings (a splitting A= M− N is nonnegative if M −1 exist and M −1 N is nonnegative) are derived. They extend the known results in the literature. In addition, we also point out three incorrect conditions in a paper by Beauwens. Furthermore, we give some reasonable conditions ensuring the strict inequality between the asymptotic convergence rates. This also answers the open question which additional and appropriate conditions should be imposed on Miller-Neumann splittings to obtain strict inequality. Finally, some applications to a class of generalized AOR, SOR, and JOR iterative methods whose special cases imply block (also point) AOR, SOR, and JOR iterative methods for solving linear systems are discussed.

Block AOR iteration for nonsymmetric matrices

We consider a class of matrices that are of interest to numerical applications and are large, sparse, but not symmetric or diagonally dominant. We give a criterion for the existence of (and we actually construct) the inverse matrix in terms of powers of a "small" matrix. We use this criterion to find that the spectral radius of the Jacobi iteration matrix, corresponding to a block tridiagonal partition, is in general ⩾ 1 \geqslant 1 . We also derive conditions (that are satisfied in cases of interest to applications) for the Jacobi matrix to have spectral radius = 1. We introduce convergent "block AOR" iterative schemes such as extrapolated Jacobi and extrapolated Gauss-Seidel schemes with optimum (under) relaxation parameter ω = .5 \omega = .5 . A numerical example pertaining to the solution of Poisson’s equation is given, as a demonstration of some of our hypotheses and results. A comparison with SOR, applied to the 5-point finite difference method, is also included.