Number of found documents: 813
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### The Equation |x| - |Ax| = b Rohn, Jiří 2020 - English We formulate conditions on A and b under which the double absolute value equation |x| - |Ax| = b possesses in each orthant a unique solution which, moreover, belongs to the interior of that orthant. Keywords: absolute value equation; double absolute value equation; orthantwise solvability; theorem of the alternatives Available in a digital repository NRGL The Equation |x| - |Ax| = b

We formulate conditions on A and b under which the double absolute value equation |x| - |Ax| = b possesses in each orthant a unique solution which, moreover, belongs to the interior of that orthant.

Rohn, Jiří
Ústav informatiky, 2020

### The scalar-valued score functions of continuous probability distribution Fabián, Zdeněk 2019 - English In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not the observed value, which is to be used in probabilistic and statistical considerations, but its 'treated form', the value of the scalar-valued score function of distribution of the assumed model. Actually, the opinion that an observed value of random variable should be 'treated' with respect to underlying model is one of main ideas of the inference based on likelihood in classical statistics. However, a vector nature of Fisher score functions of classical statistics does not enable a consistent use of this point of view. Instead, various inference functions are suggested and used in solutions of various statistical problems. Inference function of this report is the scalar-valued score function of distribution. Keywords: Shortcomings of probability theory; Scalar-valued score functions; Characteristics of continous random variables; Parametric estimation; Transformed distributions; Skew-symmetric distributions Available at various institutes of the ASCR The scalar-valued score functions of continuous probability distribution

In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not ...

Fabián, Zdeněk
Ústav informatiky, 2019

### A Logical Characteristic of Read-Once Branching Programs Žák, Stanislav 2019 - English We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two appropriate properties: i) The ”knowledge” arising at a stage of computation in question is derivable from the ”knowledge” arising at the previous stage according to the rules of the model and according to the local arrangement of the b.p. ii) The model confirms the intuitively well-known fact that the knowledge arising at a node of a computation depends not only on it but in some cases also on a ”mystery” information. (I. e. different computations reaching the same node may have different knowledge(s) arisen at it.) We prove that with respect to our model no such information exists in read-once b.p.‘s but on the other hand in b. p.‘s which are not read-once such information must be present. The read-once property forms a frontier. More concretely, we may see the instances of our models as a systems S = (U,D) where U is a universe of knowledge and D are derivation rules. We say that a b.p. P is compatible with a system S iff along each computation in P S derives F (false) or T (true) at the end correctly according to the label of the reached sink. This key notion modifies the classic paradigm which takes the computational complexity with respect to different classes of restricted b.p.‘s (e.g. read-once b.p.‘s, k-b.p.‘s, b.p.‘s computing in limited time etc.). Now, the restriction is defined by a subset of systems and only these programs are taken into account which are compatible with at least one of the chosen systems. Further we understand the sets U of knowledge(s) as a sets of admissible logical formulae. It is clear that more rich sets U‘s imply the large restrictions on b.p.‘s and consequently the smaller complexities of Boolean functions are detected. More rich logical equipment implies stronger computational effectiveness. Another question arises: given a set of Boolean functions (e.g. codes of some graphs) what logical equipment is optimal from the point of complexity? Keywords: branching programs; computational complexity; logic Available in digital repository of the ASCR A Logical Characteristic of Read-Once Branching Programs

We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two ...

Žák, Stanislav
Ústav informatiky, 2019

### Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství Rohn, Jiří 2019 - Czech V práci jsou popsány hlavní výsledky neoficiálního ekonomicko-matematického výzkumu provedeného v letech 1973-1980 pracovníky Ekonomicko-matematické laboratoře Ekonomického ústavu ČSAV a MFF (J. Bouška, J. Rohn a B. Kalendovský). Keywords: Leontěvův model; intervalová data; zaručené řešení; neexistence; matice 28 x 28 Available in digital repository of the ASCR Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství

V práci jsou popsány hlavní výsledky neoficiálního ekonomicko-matematického výzkumu provedeného v letech 1973-1980 pracovníky Ekonomicko-matematické laboratoře Ekonomického ústavu ČSAV a MFF (J. ...

Rohn, Jiří
Ústav informatiky, 2019

### Absolute Value Mapping Rohn, Jiří 2019 - English We prove a necessary and sufficient condition for an absolute value mapping to be bijective. This result simultaneously gives a characterization of unique solvability of an absolute value equation for each right-hand side. Keywords: absolute value mapping; bijectivity; interval matrix; regularity; absolute value equation; unique solvability Available in a digital repository NRGL Absolute Value Mapping

We prove a necessary and sufficient condition for an absolute value mapping to be bijective. This result simultaneously gives a characterization of unique solvability of an absolute value equation for ...

Rohn, Jiří
Ústav informatiky, 2019

### Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR Šebesta, Václav 2019 - Czech Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR Available in a digital repository NRGL Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR

Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR

Šebesta, Václav
Ústav informatiky, 2019

### Overdetermined Absolute Value Equations Rohn, Jiří 2019 - English We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case. Keywords: absolute value equations; overdetermined system Available in a digital repository NRGL Overdetermined Absolute Value Equations

We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.

Rohn, Jiří
Ústav informatiky, 2019

### Generalization of a Theorem on Eigenvalues of Symmetric Matrices Rohn, Jiří 2019 - English We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real. Keywords: symmetric matrix; positive semide nite matrix; real spectrum Available in a digital repository NRGL Generalization of a Theorem on Eigenvalues of Symmetric Matrices

We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real.

Rohn, Jiří
Ústav informatiky, 2019

### Hybrid Methods for Nonlinear Least Squares Problems Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan 2019 - English This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, together with extensive computational tests and comparisons of the introduced methods. All hybrid methods are described in detail and their global convergence is proved in a unified way. Some proofs concerning trust region methods, which are difficult to find in the literature, are also added. In particular, the report contains an analysis of a new simple hybrid method with Jacobian corrections (Section 8) and an investigation of the simple hybrid method for sparse least squares problems proposed previously in [33] (Section 14). Keywords: numerical optimization; nonlinear least squares; trust region methods; hybrid methods; sparse problems; partially separable problems; numerical experiments Available in a digital repository NRGL Hybrid Methods for Nonlinear Least Squares Problems

This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, together with ...

Ústav informatiky, 2019

### Sort Program for Real Keys with Linear Time Complexity Jiřina, Marcel 2019 - Czech In this report we present a program for sorting data structures with sorting keys as real numbers, i.e. of type "real" or "float". The basis of the program is a modification of the countingsort algorithm for reals (instead of integers). It uses a comparision-type sorting for small part of data set given. The time complexity of this part of program can be bounded by linear function of n and thus, the total time complexity is also O(n) for n data items. Keywords: sorting; real sorting keys; counting sort Available in a digital repository NRGL Sort Program for Real Keys with Linear Time Complexity

In this report we present a program for sorting data structures with sorting keys as real numbers, i.e. of type "real" or "float". The basis of the program is a modification of the countingsort ...

Jiřina, Marcel
Ústav informatiky, 2019

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