Computing the real solutions of Fleishman's equations for simulating non‐normal data

2021 ◽  
Author(s):  
Nathaniel E. Helwig
Keyword(s):  
The Real ◽  
Real Solutions

Microcomputer-Assisted Mathematics: Polynomial Equations Revisited

1986 ◽  
Vol 79 (9) ◽  
pp. 732-737
Author(s):  
Jillian C. F. Sullivan
Keyword(s):  
High School ◽  
High School Students ◽  
Numerical Methods ◽  
Polynomial Equations ◽  
School Students ◽  
The Real ◽  
Real Solutions ◽  
Quadratic Equations ◽  
Computational Difficulty

Although solving polynomial equations is important in mathematics, most high school students can solve only linear and quadratic equations. This is because the methods for solving cubic and quartic equations are difficult, and no general methods of solution are available for equations of degree higher than four. However, numerical methods can be used to approximate the real solutions of polynomial equations of any degree. Because they involve a great deal of computation they have not traditionally been taught in the schools. Now that most students have access to calculators and computers, this computational difficulty is easily overcome.

The Real Solutions to a System of Quaternion Matrix Equations with Applications

2009 ◽  
Vol 37 (6) ◽  
pp. 2060-2079 ◽  
Author(s):  
Qing-Wen Wang ◽  
Shao-Wen Yu ◽  
Qin Zhang
Keyword(s):  
Matrix Equations ◽  
Quaternion Matrix ◽  
The Real ◽  
Real Solutions

scholarly journals Exponential cosmological solutions with two factor spaces in EGB model with $$\Lambda = 0$$ revisited

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
V. D. Ivashchuk ◽  
A. A. Kobtsev
Keyword(s):  
Analytical Solutions ◽  
Gravitational Constant ◽  
Cosmological Solution ◽  
Cosmological Term ◽  
Exponential Dependence ◽  
The Real ◽  
Real Solutions ◽  
Scale Factors ◽  
Cosmological Solutions

Abstract We study exact cosmological solutions in D-dimensional Einstein–Gauss–Bonnet model (with zero cosmological term) governed by two non-zero constants: $$\alpha _1$$α1 and $$\alpha _2$$α2 . We deal with exponential dependence (in time) of two scale factors governed by Hubble-like parameters $$H >0$$H>0 and h, which correspond to factor spaces of dimensions $$m >2$$m>2 and $$l > 2$$l>2, respectively, and $$D = 1 + m + l$$D=1+m+l. We put $$h \ne H$$h≠H and $$mH + l h \ne 0$$mH+lh≠0. We show that for $$\alpha = \alpha _2/\alpha _1 > 0$$α=α2/α1>0 there are two (real) solutions with two sets of Hubble-like parameters: $$(H_1, h_1)$$(H1,h1) and $$(H_2, h_2)$$(H2,h2), which obey: $$ h_1/ H_1< - m/l< h_2/ H_2 < 0$$h1/H1<-m/l<h2/H2<0, while for $$\alpha < 0$$α<0 the (real) solutions are absent. We prove that the cosmological solution corresponding to $$(H_2, h_2)$$(H2,h2) is stable in a class of cosmological solutions with diagonal metrics, while the solution corresponding to $$(H_1, h_1)$$(H1,h1) is unstable. We present several examples of analytical solutions, e.g. stable ones with small enough variation of the effective gravitational constant G, for $$(m, l) = (9, l >2), (12, 11), (11,16), (15, 6)$$(m,l)=(9,l>2),(12,11),(11,16),(15,6).

The Real Solutions of Equation of in Control Theory

2010 ◽  
Vol 121-122 ◽  
pp. 911-915
Author(s):  
Xue Ting Liu
Keyword(s):  
Control Theory ◽  
Chemical Engineering ◽  
Research Field ◽  
Matrix Equations ◽  
The Real ◽  
Real Solutions ◽  
Nonsingular Solution ◽  
The Matrix ◽  
Active Research ◽  
Solutions Of Equations

. The research of matrix equations is an active research field, matrix equations have applied in many physical applications in recent years. As one of them, the equation is applied more and more extensively, such as control theory, chemistry and chemical engineering and so on. In this paper, motivated by [1], we give two discriminations about the real solutions of equation . The matrix is proved that it is a nonsingular solution of equation whenever are nonsingular solutions of equations at last.

scholarly journals Forward Displacement Analysis of a Non-Plane Two Coupled Degree Nine-Link Barranov Truss Based on the Hyper-Chaotic Least Square Method

10.5772/45665 ◽  
2012 ◽  
Vol 9 (1) ◽  
pp. 8 ◽  
Author(s):  
Youxin Luo ◽  
Zouxin Mou ◽  
Bing He
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Vector Method ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
The Real ◽  
Real Solutions ◽  
Constrained Equations ◽  
Sine And Cosine Functions ◽  
Forward Displacement Analysis

The hyper-chaotic least square method for finding all of the real solutions of nonlinear equations was proposed and the following displacement analysis on the 33rd non-plane 2-coupled–degree nine-link Barranov truss was completed. Four constrained equations were established by a vector method with complex numbers according to four loops of the mechanism, and four supplement equations were also established by increasing four variables and the relation of the sine and cosine functions. The established eight equations are those of the forward displacement analysis of the mechanism. In combining the least square method with hyper-chaotic sequences, a hyper-chaotic least square method based on utilizing a hyper-chaotic discrete system to obtain and locate initial points so as to find all the real solutions of the nonlinear questions was proposed. A numerical example was given. A comparison was also done with another means of finding a solution method. The results show that all of real solutions were quickly obtained, and it proves the correctness and validity of the proposed method.

The Real Solutions of xν=yx

1966 ◽  
Vol 39 (2) ◽  
pp. 108-111
Author(s):  
A. F. Beardon
Keyword(s):  
The Real ◽  
Real Solutions

Compounds of Skew-Symmetric Matrices

1964 ◽  
Vol 16 ◽  
pp. 473-478 ◽  
Author(s):  
Marvin Marcus ◽  
Adil Yaqub
Keyword(s):  
Symmetric Matrices ◽  
The Real ◽  
Real Solutions ◽  
Interesting Paper ◽  
The Matrix ◽  
Image Position ◽  
Square Matrix

In a recent interesting paper (3) H. Schwerdtfeger answered a question of W. R. Utz (4) on the structure of the real solutions A of A* = B, where A is skew-symmetric. (Utz and Schwerdtfeger call A* the "adjugate" of A ; A* is the n-square matrix whose (i, j) entry is (—1)i+j times the determinant of the (n — 1)-square matrix obtained by deleting row i and column j of A. The word "adjugate," however, is more usually applied to the matrix (AT)*, where AT denotes the transposed matrix of A ; cf. (1, 2).)The object of the present paper is to find all real n-square skew-symmetric solutions A to the equation

Sign in / Sign up

Export Citation Format

Share Document