Methods of conjugate gradients for solving linear systems

Methods of Conjugate Gradients for Solving Linear Systems

The advent of electronic computers in the middle of the 20th century stimulated a flurry of activity in developing numerical algorithms that could be applied to computational problems much more difficult than those solved in the past. The work described in this paper [1] was done at the Institute for Numerical Analysis, a part of NBS on the campus of UCLA [2]. This institute was an incredibly f...

Methods of Conjugate Gradients for Solving Linear Systems

An iterative algorithm is given for solving a system Ax= k of n linear equations in n unknowns. The solution is given in n steps . It is shown that this method is a special case of a very general met hod which also includes Gaussian elimination . These general algorithms are essentially algorithms for findin g an n dimensional ellipsoid . Connections a re m ade wit h the theory of orthogonal po...

A METHOD FOR SOLVING FUZZY LINEAR SYSTEMS

In this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. Also necessary and sufficient conditions for existenceof solution are given. Some numerical examples illustrate the efficiencyof the method.

Defuzzification method for solving fuzzy linear systems

‎Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...