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<a name="Specialized-Solvers"></a>
Previous: <a rel="previous" accesskey="p" href="Functions-of-a-Matrix.html#Functions-of-a-Matrix">Functions of a Matrix</a>,
Up: <a rel="up" accesskey="u" href="Linear-Algebra.html#Linear-Algebra">Linear Algebra</a>
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<h3 class="section">18.5 Specialized Solvers</h3>
<!-- ./sparse/bicgstab.m -->
<p><a name="doc_002dbicgstab"></a>
<div class="defun">
— Function File: <b>bicgstab</b> (<var>A, b</var>)<var><a name="index-bicgstab-1627"></a></var><br>
— Function File: <b>bicgstab</b> (<var>A, b, tol, maxit, M1, M2, x0</var>)<var><a name="index-bicgstab-1628"></a></var><br>
<blockquote><p>This procedure attempts to solve a system of linear equations A*x = b for x.
The <var>A</var> must be square, symmetric and positive definite real matrix N*N.
The <var>b</var> must be a one column vector with a length of N.
The <var>tol</var> specifies the tolerance of the method, the default value is 1e-6.
The <var>maxit</var> specifies the maximum number of iterations, the default value is min(20,N).
The <var>M1</var> specifies a preconditioner, can also be a function handler which returns M\X.
The <var>M2</var> combined with <var>M1</var> defines preconditioner as preconditioner=M1*M2.
The <var>x0</var> is the initial guess, the default value is zeros(N,1).
<p>The value <var>x</var> is a computed result of this procedure.
The value <var>flag</var> can be 0 when we reach tolerance in <var>maxit</var> iterations, 1 when
we don't reach tolerance in <var>maxit</var> iterations and 3 when the procedure stagnates.
The value <var>relres</var> is a relative residual - norm(b-A*x)/norm(b).
The value <var>iter</var> is an iteration number in which x was computed.
The value <var>resvec</var> is a vector of <var>relres</var> for each iteration.
</blockquote></div>
<!-- ./sparse/cgs.m -->
<p><a name="doc_002dcgs"></a>
<div class="defun">
— Function File: <b>cgs</b> (<var>A, b</var>)<var><a name="index-cgs-1629"></a></var><br>
— Function File: <b>cgs</b> (<var>A, b, tol, maxit, M1, M2, x0</var>)<var><a name="index-cgs-1630"></a></var><br>
<blockquote><p>This procedure attempts to solve a system of linear equations A*x = b for x.
The <var>A</var> must be square, symmetric and positive definite real matrix N*N.
The <var>b</var> must be a one column vector with a length of N.
The <var>tol</var> specifies the tolerance of the method, default value is 1e-6.
The <var>maxit</var> specifies the maximum number of iteration, default value is MIN(20,N).
The <var>M1</var> specifies a preconditioner, can also be a function handler which returns M\X.
The <var>M2</var> combined with <var>M1</var> defines preconditioner as preconditioner=M1*M2.
The <var>x0</var> is initial guess, default value is zeros(N,1).
</blockquote></div>
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