scholarly journals A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Rongrong Cui ◽  
Chuanqing Gu
Keyword(s):  
Continued Fractions ◽  
Matrix Function ◽  
Continued Fraction ◽  
Generalized Inverse ◽  
New Method ◽  
Rectangular Grid ◽  
Type Formula ◽  
The Matrix ◽  
Rational Interpolants ◽  
Better Than

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid. The rational interpolant is of the form motivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are based on the generalized inverse for a matrix which is introduced by C. Gu the author of this paper, and it is effective in continued fraction interpolation. The algorithm and some other important conclusions such as divisibility and characterization are given. In the end, two examples are also given to show the effectiveness of the algorithm. The numerical results of the second example show that the algorithm of this paper is better than the method of Thieletype matrix-valued rational interpolant in Gu (1997).

scholarly journals Alternative derivation of some regular continued fractions

1968 ◽  
Vol 8 (2) ◽  
pp. 205-212 ◽  
Author(s):  
R. F. C. Walters
Keyword(s):  
Positive Integer ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Matrix Approach ◽  
Alternative Derivation ◽  
The Matrix ◽  
Continued Fraction Expansions

In this paper we find an expression for ex as the limit of quotients associated with a sequence of matrices, and thence, by using the matrix approach to continued fractions ([5] 12–13, [2] and [4]), we derive the regular continued fraction expansions of e2/k and tan 1/k (where k is a positive integer).

A Design of High-Accuracy Displacement Measurement Instrument from Principles of Optics

2012 ◽  
Vol 170-173 ◽  
pp. 2924-2928
Author(s):  
Sheng Biao Chen ◽  
Yun Zhi Tan
Keyword(s):  
Measurement Instrument ◽  
High Accuracy ◽  
Mechanical Tests ◽  
Total Reflection ◽  
Displacement Measurement ◽  
New Method ◽  
Water Volume ◽  
Water Drainage ◽  
Accuracy Of Measurement ◽  
Better Than

In order to measure the water drainage volume in soil mechanical tests accurately, it develop a new method which is based on principles of optics. And from both physical and mathematic aspects, it deduces the mathematic relationship between micro change in displacement and the increment projected on screen. The result shows that total reflection condition is better than refraction condition. What’s more, the screen could show the water volume micro variation clearly, so it can improve the accuracy of measurement.

scholarly journals A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 255
Author(s):  
Dan Lascu ◽  
Gabriela Ileana Sebe
Keyword(s):  
Dynamical Systems ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Unit Interval ◽  
Probability Measures ◽  
Absolutely Continuous ◽  
Continued Fraction Expansions ◽  
Absolutely Continuous Invariant

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aim to compare the efficiency by describing the rate at which the digits of one number-theoretic expansion determine those of another. We study Chan’s continued fractions, θ-expansions, N-continued fractions, and Rényi-type continued fractions. A central role in fulfilling our goal is played by the entropy of the absolutely continuous invariant probability measures of the associated dynamical systems.

scholarly journals Extreme Value Theory for Hurwitz Complex Continued Fractions

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 840
Author(s):  
Maxim Sølund Kirsebom
Keyword(s):  
Invariant Measure ◽  
Extreme Value Theory ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Value Theory ◽  
Extreme Value ◽  
Poisson Law ◽  
Complex Continued Fractions

The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper, we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law and an extreme value law. The results are based on cusp estimates of the invariant measure about which information is still limited. In the process, we obtained several results concerning the extremes of nearest integer continued fractions as well.

scholarly journals A new method for identifying the role of marital preferences at shaping marriage patterns

2021 ◽  
pp. 1-27
Author(s):  
Anna Naszodi ◽  
Francisco Mendonca
Keyword(s):  
Contingency Table ◽  
Transformation Method ◽  
New Method ◽  
Marriage Patterns ◽  
The Us ◽  
Analytical Properties ◽  
The Matrix ◽  
Transformation Methods

Abstract We develop a method which assumes that marital preferences are characterized either by the scalar-valued measure proposed by Liu and Lu, or by the matrix-valued generalized Liu–Lu measure. The new method transforms an observed contingency table into a counterfactual table while preserving its (generalized) Liu–Lu value. After exploring some analytical properties of the new method, we illustrate its application by decomposing changes in the prevalence of homogamy in the US between 1980 and 2010. We perform this decomposition with two alternative transformation methods as well where both methods capture preferences differently from Liu and Lu. Finally, we use survey evidence to support our claim that out of the three considered methods, the new transformation method is the most suitable for identifying the role of marital preferences at shaping marriage patterns. These data are also in favor of measuring assortativity in preferences à la Liu and Lu.

scholarly journals Calculating astronomical refraction by means of continued fractions

1979 ◽  
Vol 89 ◽  
pp. 95-101
Author(s):  
S. Mikkola
Keyword(s):  
Asymptotic Expansion ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Astronomical Refraction

A continued fraction was derived for the summation of the asymptotic expansion of astronomical refraction. Using simple approximations for the last denominator of the fraction, accurate formulae, useful down to the horizon, were obtained. The method is not restricted to any model of the atmosphere and can thus be used in calculations based on actual aerological measurements.

Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 2 - Case Studies

2021 ◽  
Author(s):  
Sathya Prasad Mangalaramanan
Keyword(s):  
Lower Bound ◽  
Case Studies ◽  
Power Law ◽  
Elastic Moduli ◽  
New Method ◽  
Stress Distributions ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Thick Cylinder ◽  
Better Than

Abstract An accompanying paper provides the theoretical underpinnings of a new method to determine statically admissible stress distributions in a structure, called Bounded elastic moduli multiplier technique (BEMMT). It has been shown that, for textbook cases such as thick cylinder, beam, etc., the proposed method offers statically admissible stress distributions better than the power law and closer to elastic-plastic solutions. This paper offers several examples to demonstrate the robustness of this method. Upper and lower bound limit loads are calculated using iterative elastic analyses using both power law and BEMMT. These results are compared with the ones obtained from elastic-plastic FEA. Consistently BEMMT has outperformed power law when it comes to estimating lower bound limit loads.

Dosage du Sr-90 dans l'eau des lacs et des rivières du Québec par précipitation avec l'oxine et comptage β

1988 ◽  
Vol 66 (1) ◽  
pp. 174-177 ◽  
Author(s):  
E. Haddad ◽  
L. Zikovsky
Keyword(s):  
Detection Limit ◽  
Surface Waters ◽  
New Method ◽  
The Mean ◽  
Better Than

A new method for the determination of Sr-90 dissolved in surface waters has been developed. It is based on the precipitation of Sr with 8-hydroxyquinoline at pH 11.3 and counting of β particles with energy above 150 keV. The detection limit obtained is 0.5 mBq/L and the mean yield is 28%. The decontamination factors from other β emitters achieved are better than 10 000. This method has been used to measure the Sr-90 in 5 lakes and 5 rivers in Québec and activities ranging from 3 to 15 mBq/L were obtained. This new method is as efficient and reliable as conventional techniques while being less tedious.

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