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LinearFixPointEquationSystem.java
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// FILE. . . . . d:/hak/hlt/src/hlt/math/matrix/sources/LinearFixPointEquationSystem.java // EDIT BY . . . Hassan Ait-Kaci // ON MACHINE. . Hak-Laptop // STARTED ON. . Sat Nov 16 15:03:29 2019
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package hlt.math.matrix;
| package hlt.math.matrix documentation listing |
This implements a system of linear fix-point equations with double
coefficients of the form:
A × X + B = X where A is an m
× n Matrix, B is an
m × 1 Matrix (i.e., a
column vector of order m), and X is a column vector
of order n of variables Xi,
i=1, ... n. For example, if m = 3, n = 4
and:
1.1 1.2 1.3 1.4 1.0
A = 2.1 2.2 2.3 2.4 B = 2.0
3.1 3.2 3.3 3.4 3.0
then:
1.1 × X1 + 1.2 × X2 + 1.3 × X3 + 1.4 × X4 + 1.0 = X1
2.1 × X1 + 2.2 × X2 + 2.3 × X3 + 2.4 × X4 + 2.0 = X2
3.1 × X1 + 3.2 × X2 + 3.3 × X3 + 3.4 × X4 + 3.0 = X3
which gives the equivalent non-fix-point formulation (A-I) × X = -B:
0.1 × X1 + 1.2 × X2 + 1.3 × X3 + 1.4 × X4 = -1.0
2.1 × X1 + 1.2 × X2 + 2.3 × X3 + 2.4 × X4 = -2.0
3.1 × X1 + 3.2 × X2 + 2.3 × X3 + 3.4 × X4 = -3.0
and conversely, from the more conventional non-fix-point
formulation of the form A' × X = B', one recovers the
corresponding equivalent fix-point form as:
(A'+I) × X + (-B') = X, and then use this class.
Non square equational systems may only have parametric solutions if
there are more variables than equations (expressed in terms of the
missing variables), or redundant solutions if there are more
equations than variables. For a square matrix, a solution will exist
iff it has an inverse (i.e., iff it has a non-zero
determinant).
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public class LinearFixPointEquationSystem { }
This file was generated on Wed Dec 18 03:37:41 PST 2019 from file LinearFixPointEquationSystem.java
by the hlt.language.tools.Hilite Java tool written by Hassan Aït-Kaci