Nela Bosner

• University of Zagreb

After its reintroduction in northern Croatia, the Eurasian beaver (Castor fiber L.) successfully spread to new areas along streams. Although the beaver has spread in a part of Croatia covered with karst, the information published to date about beavers using caves has been sparse. Since the first observation in the Matešićeva Cave-Popovačka Cave Sys...

After its reintroduction in northern Croatia, the Eurasian beaver (Castor fiber L.) successfully spread to new areas along streams. Although the beaver has spread in a part of Croatia covered with karst, the information published to date about beavers using caves has been sparse. Since the first observation in the Matešićeva Cave – Popovačka Cave S...

Joint approximate diagonalization (JAD) of multiple matrices is a core problem in many applications. In this work we propose two numerical methods for computing JAD, based on constrained optimization on two different matrix manifolds, with emphasis on their numerical properties and efficiency. Our goal is to solve efficiently the following problem:...

The VZ algorithm proposed by Charles F. Van Loan (SIMA, 1975) attempts to solve the generalized type of matrix eigenvalue problem ACx = λBDx, where A, B ∈ Rn×m, C, D ∈ Rm×n, and m ≥ n, without forming products and inverses. Especially, this algorithm is suitable for solving the generalized singular value problem. Van Loan’s approach first reduces t...

Prony's method is a standard tool exploited for solving many imaging and data analysis problems that result in parameter identification in sparse exponential sums $$f(k)=\sum_{j=1}^{T}c_{j}e^{-2\pi i\langle t_{j},k\rangle},\quad k\in \mathbb{Z}^{d},$$ where the parameters are pairwise different $\{ t_{j}\}_{j=1}^{M}\subset [0,1)^{d}$, and $\{ c_{j}...

This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple right-hand sides. Such problems often appear e.g. in control theory when evaluating the transfer function, or as a part...

This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple right-hand sides. Such problems often appear e.g. in control theory when evaluating the transfer function, or as a part...

Several problems from control theory are presented which are sensitive to badly scaled matrices. We were specially concerned with the algorithms involving three matrices, thus we extended the Ward's balancing algorithm for two matrices. Numerical experiments confirmed that balancing three matrices can produce an accurate frequency response matrix f...

This paper proposes an efficient algorithm for simultaneous reduction of three matrices by using orthogonal transformations, where A is reduced to m-Hessenberg form, and B and E to triangular form. The algorithm is a blocked version of the algorithm described by Miminis and Paige (Int J Control 35:341–354, 1982). The m-Hessenberg-triangular–triangu...

This article proposes an efficient algorithm for reducing matrices to generalized Hessenberg form by unitary similarity, and recommends using it as a preprocessor in a variety of applications. To illustrate its usefulness, two cases from control theory are analyzed in detail: a solution procedure for a sequence of shifted linear systems with multip...

Large-scale eigenvalue and singular value computations are usually based on extracting information from a compression of the matrix to suitably chosen low dimensional subspaces. This paper introduces new a posteriori relative error bounds based on a residual expressed using the largest principal angle (gap) between relevant subspaces. The eigenvect...

Inverse iteration is simple but not very efficient method for computing few eigenvalues with minimal absolute values and corresponding eigenvectors of a symmetric matrix. The idea is to increase its efficiency by technique similar to multigrid methods used for solving linear systems. This approach is not new, but until now multigrid was mostly used...

Two new algorithms for one-sided bidiagonalization are presented. The first is a block version which improves execution time by improving cache utilization from the use of BLAS 2.5 operations and more BLAS 3 operations. The second is adapted to parallel computation. When incorporated into singular value decomposition software, the second algorithm...

A new bidiagonal reduction method is proposed for X∈Rm×n. For m⩾n, it decomposes X into the product X=UBVT where U∈Rm×n has orthonormal columns, V∈Rn×n is orthogonal, and B∈Rn×n is upper bidiagonal. The matrix V is computed as a product of Householder transformations. The matrices U and B are constructed using a recurrence. If U is desired from the...

The singular value decomposition (SVD) of a general matrix is the fundamental theoretical and computational tool in numerical linear algebra. The most efficient way to compute the SVD is to reduce the matrix to bidiagonal form in a finite number of orthogonal (unitary) transformations, and then to compute the bidiagonal SVD. This paper gives detail...

Very often used methods for solving linear systems are Krylov subspace iterative methods. Usually, the iterations stop at the moment when some norm of the residual reaches a tolerable value. Since all computations are done in finite precision arithmetic, we can check only some approximation of the residual norm. The main goal of our research is to...