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Dive into the research topics where Josip Matejaš is active.

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Featured researches published by Josip Matejaš.


Numerische Mathematik | 2000

Quadratic convergence of scaled matrices in Jacobi method

Josip Matejaš

Summary. A quadratic convergence bound for scaled Jacobi iterates is proved provided the initial symmetric positive definite matrix has simple eigenvalues. The bound is expressed in terms of the off-norm of the scaled initial matrix and the minimum relative gap in the spectrum. The obtained result can be used to predict the stopping moment in the two-sided and especially in the one-sided Jacobi method.


Applied Mathematics and Computation | 2014

A new iterative method for solving multiobjective linear programming problem

Josip Matejaš; Tunjo Perić

In the paper we present a new iterative method for solving multiobjective linear programming problems with an arbitrary number of decision makers. The method is based on the principles of game theory. Each step of the method yields a unique solution which respects the aspirations of decision makers within the frame of given possibilities. Each decision maker is assigned an objective indicator which shows the reality of his aspiration and which may be used to define the strategy for the next step. The method can be easily extended to general (nonlinear) multiobjective programming problems but the numerical application would require further research on computational methods.


Applied Mathematics and Computation | 2010

Accuracy of the Kogbetliantz method for scaled diagonally dominant triangular matrices

Josip Matejaš; Vjeran Hari

The paper proves that Kogbetliantz method computes all singular values of a scaled diagonally dominant triangular matrix, which can be well scaled from both sides symmetrically, to high relative accuracy. Special attention is paid to deriving sharp accuracy bounds for one step, one batch and one sweep of the method. By a simple numerical test it is shown that the methods based on bidiagonalization are generally not accurate on that class of well-behaved matrices.


Archive | 2003

Quadratic Convergence of Scaled Iterates by Kogbetliantz Method

Vjeran Hari; Josip Matejaš

A sharp quadratic convergence bound of scaled iterates for the serial Kogbetliantz method is derived. Iterates are symmetrically scaled by diagonal matrices so that diagonal elements are ones. The result is obtained for a scaled diagonally dominant complex triangular matrix with multiple singular values. The estimate depends on the relative separation of the singular values.


Applied Mathematics and Computation | 2009

Accuracy of two SVD algorithms for 2×2 triangular matrices

Vjeran Hari; Josip Matejaš

A new algorithm for the accurate computation of the singular value decomposition of 2x2 triangular matrices is proposed. The algorithm is based on Voevodin formulas. Sharp accuracy bounds are derived by using a subtle error analysis which tracks the signs of the errors of intermediate quantities and does not neglect the non-linear parts of the errors. The analysis is fine tuned for the case of almost diagonal matrices. The same analysis is also used to analyze the errors for the xLASV2 computational routine of LAPACK. The error estimates of the new algorithm compare favorably to those of the LAPACK routine.


Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik | 1998

Scaled Almost Diagonal Matrices with Multiple Singular Values

Josip Matejaš; Vjeran Hari

New estimate for relative distances between the singular values and the moduli of the appropriate diagonal elements of a scaled almost diagonal square matrix are derived. In case of a multiple singular value the bounds also estimate the structure of the diagonal block associated with that singular value. The bounds are expressed in terms of the off-diagonal elements of an appropriately scaled matrix, and of relative gaps between singular values. The new estimates refine the existing ones which are based on the absolute gaps between singular values. They are especially appropriate for the smallest singular values. For triangular and essentially triangular matrices, the new bounds take simple and applicable form.


Linear Algebra and its Applications | 2002

Convergence of scaled iterates by the Jacobi method

Josip Matejaš

Abstract A quadratic convergence bound for scaled iterates by the serial Jacobi method for Hermitian positive definite matrices is derived. By scaled iterates we mean the matrices [diag( H ( k ) )] −1/2 H ( k ) [diag( H ( k ) )] −1/2 , where H ( k ) , k ⩾0, are matrices generated by the method. The bound is obtained in the general case of multiple eigenvalues. It depends on the minimum relative separation of the eigenvalues.


Numerical Algorithms | 2015

Accuracy of one step of the Falk-Langemeyer method

Josip Matejaš

We present a new subtle technique in accuracy analysis which we use to prove the accuracy of the Falk-Langemeyer method for solving a real definite generalized eigenvalue problem Ax=λBx. We derive the exact expressions for the errors caused by finite arithmetic computation in one step of the method. We consider separately the case of diagonal, positive definite matrix B


Central European Journal of Operations Research | 2018

Comparative analysis of application efficiency of two iterative multi objective linear programming methods (MP method and STEM method)

Tunjo Perić; Zoran Babić; Josip Matejaš

In this paper we consider a production plan optimization problem for a company that produces textile products. The problem is solved using two iterative methods: a new method based on the cooperative game theory (MP method) and the well-known STEM method. Their application efficiency and the solutions obtained are compared. For this purpose we use four groups of criteria: (1) the general characteristics of the method (2) the criteria from the standpoint of the decision makers, (3) the criteria from the perspective of the analysts, and (4) the ‘economic’ criteria. The analysis indicates that both methods are highly efficient for solving this kind of production plan optimization problems. However, the decision-makers preferred the MP method.


International journal of engineering business management | 2015

An Application of the MP Method for Solving the Problem of Distribution

Tunjo Perić; Josip Matejaš

In this paper, we present an application of a method for solving the multi-objective programming problem (the MP method), which was introduced in [1]. This method is used to solve the problem of distribution (te problem of cost/profit allocation). The method is based on the principles of cooperative games and linear programming. In the paper, we consider the standard case (proportional distribution) and the generalized case in which the basic ideas of coalitions have been incorporated. The presented theory is applied and explained on an investment model for economic recovery.

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