On the efficient update of rectangular LU-factorizations subject to low rank modifications.

Stange, Peter; Griewank, Andreas; Bollhöfer, Matthias

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Displaying similar documents to “On the efficient update of rectangular LU-factorizations subject to low rank modifications.”

A linear programming based analysis of the CP-rank of completely positive matrices

Yingbo Li, Anton Kummert, Andreas Frommer (2004)

International Journal of Applied Mathematics and Computer Science

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A real matrix A is said to be completely positive (CP) if it can be decomposed as A = BB^T, where the real matrix B has exclusively non-negative entries. Let k be the rank of A and Φ_k the least possible number of columns of the matrix B, the so-called completely positive rank (cp-rank) of A. The present work is devoted to a study of a general upper bound for the cp-rank of an arbitrary completely positive matrix A and its dependence on the ordinary rank k. This general upper bound of...

A new diagonal quasi-Newton algorithm for unconstrained optimization problems

Mahsa Nosrati, Keyvan Amini (2024)

Applications of Mathematics

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We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods.

M₂-rank differences for overpartitions

Jeremy Lovejoy, Robert Osburn (2010)

Acta Arithmetica

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On superlinear multiplier update methods for partial augmented Lagrangian techniques.

Eugenio Mijangos (2002)

Qüestiió

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The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function, including only the nonlinear constraints. This procedure is particularly interesting in case that the linear constraints are flow conservation equations, as there exist efficient techniques to solve nonlinear network problems. It is then necessary to estimate their multipliers, and variable reduction techniques can be used to...

Efficient numerical algorithms for balanced stochastic truncation

Peter Benner, Enrique Quintana-Ortí, Gregorio Quintana-Ortí (2001)

International Journal of Applied Mathematics and Computer Science

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We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses full-rank factors of the Gramians to be balanced versus each other and exploits the fact that for large-scale systems these Gramians are often of low numerical rank. We use the easy-to-parallelize sign function method as the major computational tool in determining these full-rank factors and demonstrate the numerical performance of the suggested implementation...

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that $rank (P^{*} A Q) = rank (P^{*} A) + rank (A Q) - rank (A),$ where $A$ is idempotent, $[P, Q]$ has full row rank and $P^{*} Q = 0$ . Some applications of the rank formula to generalized inverses of matrices are also presented.

Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction.

Kruk, Serge, Wolkowicz, Henry (2003)

Journal of Applied Mathematics

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Extra multistep BFGS updates in quasi-Newton methods.

Moghrabi, Issam A.R. (2006)

International Journal of Mathematics and Mathematical Sciences

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Rank conditions for estimability of covariances

G. S. Rogers (1983)

Applicationes Mathematicae

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