Results 261 to 270 of about 313,126 (308)
Some of the next articles are maybe not open access.
Overdetermined Systems of Linear Equations
SIAM Review, 1963for all x we call a Cebysev (approximate) solution (for short, C.S.) of (1).3 This report is a study of the properties of Cebysev solutions of (1). Most of the results we shall obtain may be found, explicitly or implicitly, in the literature. In particular this exposition relies on the presentations of Rivlin and Shapiro [1] and of Rademacher and ...
openaire +1 more source
2021
The system of m linear equations with n unknowns is written as $$\displaystyle \left \{ \begin {array}{rcl} a_{11}x_1+a_{12}x_2+\dots +a_{1n}x_n & = & b_1,\\ a_{21}x_1+a_{22}x_2+\dots +a_{2n}x_n & = & b_2,\\ \hdotsfor {3}{12.5pc}\\ a_{m1}x_1+a_{m2}x_2+\dots +a_{mn}x_n & = & b_m. \end {array} \right . $$
Sergei Kurgalin, Sergei Borzunov
openaire +1 more source
The system of m linear equations with n unknowns is written as $$\displaystyle \left \{ \begin {array}{rcl} a_{11}x_1+a_{12}x_2+\dots +a_{1n}x_n & = & b_1,\\ a_{21}x_1+a_{22}x_2+\dots +a_{2n}x_n & = & b_2,\\ \hdotsfor {3}{12.5pc}\\ a_{m1}x_1+a_{m2}x_2+\dots +a_{mn}x_n & = & b_m. \end {array} \right . $$
Sergei Kurgalin, Sergei Borzunov
openaire +1 more source
Solvability of Systems of Linear Interval Equations
SIAM Journal on Matrix Analysis and Applications, 2003Summary: A system of linear interval equations is called solvable if each system of linear equations contained therein is solvable. In the main result of this paper it is proved that solvability of a general rectangular system of linear interval equations can be characterized in terms of nonnegative solvability of a finite number of systems of linear ...
openaire +2 more sources
On Systems of Linear Differential Equations
American Journal of Mathematics, 1951with U a column vector and A and P n-square matrices. The transformation U = TU, by a unimodular matrix T is easily seen to result in an equation in U, of form (1), in which the coefficient of A is T-1AT. It is known [1] that if the elements of A and its characteristic roots are holomorphic in a closed bounded region R, then there exists a matrix T ...
openaire +1 more source
2001
In this chapter, we always assume that the linalg library has been loaded with the command with (linalg).
Jack-Michel Cornil, Philippe Testud
openaire +1 more source
In this chapter, we always assume that the linalg library has been loaded with the command with (linalg).
Jack-Michel Cornil, Philippe Testud
openaire +1 more source
2016
A linear equation in \(\mathbb {R}\) in the variables \(x_1,x_2,\ldots ,x_n\) is an equation of the kind:
openaire +2 more sources
A linear equation in \(\mathbb {R}\) in the variables \(x_1,x_2,\ldots ,x_n\) is an equation of the kind:
openaire +2 more sources
1991
Many problems in mathematics lead to linear systems of equations. In fact, in using computers to solve such problems, we frequently encounter very large linear systems. Thus, the development of efficient algorithms to solve such systems is of central importance in numerical analysis. We differentiate between two types of methods.
Günther Hämmerlin, Karl-Heinz Hoffman
openaire +1 more source
Many problems in mathematics lead to linear systems of equations. In fact, in using computers to solve such problems, we frequently encounter very large linear systems. Thus, the development of efficient algorithms to solve such systems is of central importance in numerical analysis. We differentiate between two types of methods.
Günther Hämmerlin, Karl-Heinz Hoffman
openaire +1 more source
Linear and non-linear equations and equation systems
2023Md Rejwanur Rashid Mojumdar +1 more
openaire +1 more source
2000
Consider the system of linear equations $$\displaystyle{ Ax = b, }$$ (3.1) where A is m × n and b is an m-element vector.
openaire +1 more source
Consider the system of linear equations $$\displaystyle{ Ax = b, }$$ (3.1) where A is m × n and b is an m-element vector.
openaire +1 more source
2011
Remember the economic model given in Introduction. It is one of the main problems in economics to find when (i.e, under what price) the demand and the supply of the economic system will be in equilibrium. We now begin to find these conditions for our model in the most general way.
Fuad Aleskerov +2 more
openaire +1 more source
Remember the economic model given in Introduction. It is one of the main problems in economics to find when (i.e, under what price) the demand and the supply of the economic system will be in equilibrium. We now begin to find these conditions for our model in the most general way.
Fuad Aleskerov +2 more
openaire +1 more source