Results 131 to 140 of about 1,955,543 (186)
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1978
In the historical development of linear algebra the geometry of linear transformations and the algebra of systems of linear equations played significant and important roles. A system of linear equations has the form $$\begin{gathered} {{a}_{{1,1}}}{{x}_{1}} + {{a}_{{1,2}}}{{x}_{2}} + \cdots + {{a}_{{1,n}}}{{x}_{n}} = {{b}_{1}}, \hfill \\ {{a}_{{2,1}
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In the historical development of linear algebra the geometry of linear transformations and the algebra of systems of linear equations played significant and important roles. A system of linear equations has the form $$\begin{gathered} {{a}_{{1,1}}}{{x}_{1}} + {{a}_{{1,2}}}{{x}_{2}} + \cdots + {{a}_{{1,n}}}{{x}_{n}} = {{b}_{1}}, \hfill \\ {{a}_{{2,1}
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1995
The theory of finite-dimensional vector spaces was created primarily in connection with one problem, and that is the simultaneous solution of a system of k linear equations in n indeterminates over a field F of the form $$ \begin{gathered} {a_{11}}{X_1} + ... + {a_{1n}}{X_n} = {b_1} \hfill \\ {a_{21}}{X_1} + ...
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The theory of finite-dimensional vector spaces was created primarily in connection with one problem, and that is the simultaneous solution of a system of k linear equations in n indeterminates over a field F of the form $$ \begin{gathered} {a_{11}}{X_1} + ... + {a_{1n}}{X_n} = {b_1} \hfill \\ {a_{21}}{X_1} + ...
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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 ...
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2018
Linear equations and system of them are ubiquitous and an important tool in all of physics. In this chapter we shall present a systematic approach to them and to methods for their solutions.
Giovanni Landi, Alessandro Zampini
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Linear equations and system of them are ubiquitous and an important tool in all of physics. In this chapter we shall present a systematic approach to them and to methods for their solutions.
Giovanni Landi, Alessandro Zampini
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2001
In this chapter, we always assume that the linalg library has been loaded with the command with (linalg).
Jack-Michel Cornil, Philippe Testud
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In this chapter, we always assume that the linalg library has been loaded with the command with (linalg).
Jack-Michel Cornil, Philippe Testud
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2016
A linear equation in \(\mathbb {R}\) in the variables \(x_1,x_2,\ldots ,x_n\) is an equation of the kind:
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A linear equation in \(\mathbb {R}\) in the variables \(x_1,x_2,\ldots ,x_n\) is an equation of the kind:
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2000
Consider the system of linear equations $$\displaystyle{ Ax = b, }$$ (3.1) where A is m × n and b is an m-element vector.
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Consider the system of linear equations $$\displaystyle{ Ax = b, }$$ (3.1) where A is m × n and b is an m-element vector.
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2014
Solving a system of linear equations is one of the most frequent tasks in numerical computing. The reason is twofold: historically, many phenomena in physics and engineering have been modeled by linear differential equations, since they are much easier to analyze than nonlinear ones.
Walter Gander +2 more
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Solving a system of linear equations is one of the most frequent tasks in numerical computing. The reason is twofold: historically, many phenomena in physics and engineering have been modeled by linear differential equations, since they are much easier to analyze than nonlinear ones.
Walter Gander +2 more
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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
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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
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1993
Finding the solution of a linear system of equations is one of the basic problems in numerical algebra. We will develop a verification algorithm for square systems with full matrix based on a Newton-like method for an equivalent fixed-point problem.
Ulrich Kulisch +3 more
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Finding the solution of a linear system of equations is one of the basic problems in numerical algebra. We will develop a verification algorithm for square systems with full matrix based on a Newton-like method for an equivalent fixed-point problem.
Ulrich Kulisch +3 more
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