Inverse of Interval Matrix and Solution of System of Equations with Interval Coefficient (Using Modified Interval Arithmetic)

Using the generalized interval arithmetic we give a generalized cholesky decomposition. Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals providing better algebraic properties. In particular, the generalized interval arithmetic is a group for addition and for multiplication of zero free intervals. These properties allow one constructing a cholesky decomposition of a generalized interval matrix A: the computed generalized interval matrix L satisfy A=LLTwith equality instead of the weaker inclusion obtained in the context of classical intervals.

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An estimate of the absolute value and width of the solution of a linear system of equations with tridiagonal interval matrix by the interval sweep method

Reliable Computing ◽

10.1007/bf02391684 ◽

1995 ◽

Vol 1 (4) ◽

pp. 393-401

Author(s):

A. N. Ostylovsky

Keyword(s):

Linear System ◽

Interval Matrix ◽

System Of Equations ◽

Sweep Method ◽

Absolute Value ◽

Linear System Of Equations ◽

The Absolute

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The RANGE family of propagation operations for intervals on simultaneous linear equations

Artificial intelligence for engineering design analysis and manufacturing ◽

10.1017/s0890060400002420 ◽

1995 ◽

Vol 9 (3) ◽

pp. 183-196 ◽

Cited By ~ 4

Author(s):

R. Chen ◽

A.C. Ward

Keyword(s):

Interval Arithmetic ◽

Linear Equations ◽

Interval Matrix ◽

Design Problems ◽

The Matrix ◽

Simultaneous Linear Equations ◽

Systems Of Linear Equations ◽

Mathematics Community

AbstractInterval arithmetic has been extensively applied to systems of linear equations by the interval matrix arithmetic community. This paper demonstrates through simple examples that some of this work can be viewed as particular instantiations of an abstract “design operation,” the RANGE operation of the Labeled Interval Calculus formalism for inference about sets of possibilities in design. These particular operations promise to solve a variety of design problems that lay beyond the reach of the original Labeled Interval Calculus. However, the abstract view also leads to a new operation, apparently overlooked by the matrix mathematics community, that should also be useful in design; the paper provides an algorithm for computing it.

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Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space

TEMA (São Carlos) ◽

10.5540/tema.2016.017.03.0283 ◽

2016 ◽

Vol 17 (3) ◽

pp. 283

Author(s):

Abdelouahab Kenoufi

Keyword(s):

Vector Space ◽

Linear Algebra ◽

Free Algebra ◽

Interval Arithmetic ◽

Differential Calculus ◽

Interval Matrix ◽

Semi Group ◽

New Approach ◽

Group Completion ◽

And Function

In this paper one proposes to use a new approach of interval arithmetic, the so-called pseudo- intervals [1, 5, 13]. It uses a construction which is more canonical and based on the semi-group completion into the group, and it allows to build a Banach vector space. This is achieved by embedding the vector space into free algebra of dimensions higher than 4. It permits to perform linear algebra and differential calculus with pseudo-intervals. Some numerical applications for interval matrix eigenmode calculation, inversion and function minimization are exhibited for simple examples.

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Canonical Submersion and Lie Homomorphisms Normal Subgroup

Nonlinear Phenomena in Complex Systems ◽

10.33581/1561-4085-2020-23-1-97-101 ◽

2020 ◽

Vol 23 (1) ◽

pp. 97-101

Author(s):

Mikhail Petrichenko ◽

Dmitry W. Serow

Keyword(s):

Normal Subgroup ◽

Canonical System ◽

System Of Equations ◽

Core Group ◽

The Core ◽

Switch Group

Normal subgroup module f (module over the ring F = [ f ] 1; 2-diffeomorphisms) coincides with the kernel Ker Lf derivations along the field. The core consists of the trivial homomorphism (integrals of the system v = x = f (t; x )) and bundles with zero switch group Lf , obtained from the condition ᐁ( ω × f ) = 0. There is the analog of the Liouville for trivial immersion. In this case, the core group Lf derivations along the field replenished elements V ( z ), such that ᐁz = ω × f. Hence, the core group Lf updated elements helicoid (spiral) bundles, in particular, such that f = ᐁU. System as an example Crocco shown that the canonical system does not permit the trivial embedding: the canonical system of equations are the closure of the class of systems that permit a submersion.

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LIQUIDUS THERMO-BAROMETER FOR THE MODELING OF MAGNETITE — MELT EQUILIBRIUM

Moscow University Bulletin. Series 4. Geology ◽

10.33623/0579-9406-2018-1-71-80 ◽

2018 ◽

pp. 71-80

Author(s):

N. S. Aryaeva ◽

E. V. Koptev-Dvornikov ◽

D. A. Bychkov

Keyword(s):

Experimental Data ◽

Liquidus Temperature ◽

Vertical Structure ◽

Maximum Error ◽

Silicate Melt ◽

System Of Equations ◽

Wide Range ◽

Basaltic Melts ◽

Multidimensional Statistics

A system of equations of thermobarometer for magnetite-silicate melt equilibrium was obtained by method of multidimensional statistics of 93 experimental data of a magnetite solubility in basaltic melts. Equations reproduce experimental data in a wide range of basalt compositions, temperatures and pressures with small errors. Verification of thermobarometers showed the maximum error in liquidus temperature reproducing does not exceed ±7 °C. The level of cumulative magnetite appearance in the vertical structure of Tsypringa, Kivakka, Burakovsky intrusions predicted with errors from ±10 to ±50 m.

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Study on the Modes of Operation of a Multi-Machine Installations with Mechanical Reduction

Alternative Energy and Ecology (ISJAEE) ◽

10.15518/isjaee.2019.10-12.012-022 ◽

2019 ◽

pp. 12-22

Author(s):

A. M. Oleynikov ◽

L. N. Kanov

Keyword(s):

Mathematical Description ◽

Reactive Power ◽

Maximum Efficiency ◽

Wind Flow ◽

System Of Equations ◽

Mechanical Equilibrium ◽

Synchronous Generators ◽

Electromagnetic Excitation ◽

Number Of Generators ◽

Wide Range

The paper gives the description of the original wind electrical installation with mechanical reduction in which the output of vertical axis wind turbine with rather low rotation speed over multiplicator is distributed to a certain number of generators. The number of acting generators is determined by the output of actual operating wind stream at each moment. According to this constructive scheme, it is possible to provide effective and with maximum efficiency installation work in a wide range of wind speeds and under any schedule issued to the consumer of electricity. As there are no any experience in using such complexes, mathematical description of its main elements is given, namely windwheels, generators with electromagnetic excitation of magnetic electrical type, then their interaction with windwheel, and also the results of mathematical modeling of work system regimes under using the offered system of equations. The basis for the mathematical description of the main elements of the installation – synchronous generators – are the system of equations of electrical and mechanical equilibrium in relative units in rotating coordinates without considering saturation of the magnetic circuit. The equation of mechanical equilibrium systems includes torque and brake windwheel electromagnetic moments of generators with taking into account the reduction coefficients and friction. In addition, we specify the alternator rotor dynamics resulting from continuous torque of windwheel fluctuations under the influence of unsteady wind flow and wind speed serving as the original variable is modeled by a set of sinusoids. Model simplification is achieved by equivalization of similar generators and by disregarding these transitions with a small time constant. Calculation the installation with synchronous generators of two types of small and medium capacity taking into account the operational factors allowed us to demonstrate the logic of interactions in the main elements of the reported complex in the process of converting wind flow into the generated active and reactive power. We have shown the possibility of stable system work under changeable wind stream condition by regulating of the plant blade angle and with simultaneous varying of generator number of different types. All these are in great interest for project organizations and power producers.

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