Doc: highlight what xPOEQUB actually does

Replace the function description taken from xPOEQU, highlight that
scaling factors computed by xPOEQUB do not introduce round-off errors,
and fix the function name in the description.

diff --git a/SRC/cpoequb.f b/SRC/cpoequb.f
index e0f4742..bf86d1a 100644 (file)
--- a/SRC/cpoequb.f
+++ b/SRC/cpoequb.f
@@ -37,12 +37,12 @@
 *>
 *> CPOEQUB computes row and column scalings intended to equilibrate a
 *> symmetric positive definite matrix A and reduce its condition number
-*> (with respect to the two-norm).  S contains the scale factors,
-*> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
-*> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
-*> choice of S puts the condition number of B within a factor N of the
-*> smallest possible condition number over all possible diagonal
-*> scalings.
+*> (with respect to the spectral norm). S contains the scale factors,
+*> chosen so that the scaled matrix B with elements
+*> B(i,j) = S(i)*A(i,j)*S(j) has diagonal entries close to one. S(i) is
+*> a power of b nearest to but not exceeding 1/sqrt(A(i,i)), where b is
+*> the basis use for floating point numbers on this machine. This choice
+*> of S avoids round-off errors when computing B.
 *> \endverbatim
 *
 *  Arguments:
@@ -151,8 +151,6 @@
 *
 *     Test the input parameters.
 *
-*     Positive definite only performs 1 pass of equilibration.
-*
       INFO = 0
       IF( N.LT.0 ) THEN
          INFO = -1

diff --git a/SRC/dpoequb.f b/SRC/dpoequb.f
index fcee160..d236914 100644 (file)
--- a/SRC/dpoequb.f
+++ b/SRC/dpoequb.f
@@ -34,14 +34,14 @@
 *>
 *> \verbatim
 *>
-*> DPOEQU computes row and column scalings intended to equilibrate a
+*> DPOEQUB computes row and column scalings intended to equilibrate a
 *> symmetric positive definite matrix A and reduce its condition number
-*> (with respect to the two-norm).  S contains the scale factors,
-*> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
-*> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
-*> choice of S puts the condition number of B within a factor N of the
-*> smallest possible condition number over all possible diagonal
-*> scalings.
+*> (with respect to the spectral norm). S contains the scale factors,
+*> chosen so that the scaled matrix B with elements
+*> B(i,j) = S(i)*A(i,j)*S(j) has diagonal entries close to one. S(i) is
+*> a power of b nearest to but not exceeding 1/sqrt(A(i,i)), where b is
+*> the basis use for floating point numbers on this machine. This choice
+*> of S avoids round-off errors when computing B.
 *> \endverbatim
 *
 *  Arguments:

diff --git a/SRC/spoequb.f b/SRC/spoequb.f
index 523aee0..6bdbcda 100644 (file)
--- a/SRC/spoequb.f
+++ b/SRC/spoequb.f
@@ -34,14 +34,14 @@
 *>
 *> \verbatim
 *>
-*> SPOEQU computes row and column scalings intended to equilibrate a
+*> SPOEQUB computes row and column scalings intended to equilibrate a
 *> symmetric positive definite matrix A and reduce its condition number
-*> (with respect to the two-norm).  S contains the scale factors,
-*> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
-*> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
-*> choice of S puts the condition number of B within a factor N of the
-*> smallest possible condition number over all possible diagonal
-*> scalings.
+*> (with respect to the spectral norm). S contains the scale factors,
+*> chosen so that the scaled matrix B with elements
+*> B(i,j) = S(i)*A(i,j)*S(j) has diagonal entries close to one. S(i) is
+*> a power of b nearest to but not exceeding 1/sqrt(A(i,i)), where b is
+*> the basis use for floating point numbers on this machine. This choice
+*> of S avoids round-off errors when computing B.
 *> \endverbatim
 *
 *  Arguments:

diff --git a/SRC/zpoequb.f b/SRC/zpoequb.f
index c0d180c..bc4ff79 100644 (file)
--- a/SRC/zpoequb.f
+++ b/SRC/zpoequb.f
@@ -37,12 +37,12 @@
 *>
 *> ZPOEQUB computes row and column scalings intended to equilibrate a
 *> symmetric positive definite matrix A and reduce its condition number
-*> (with respect to the two-norm).  S contains the scale factors,
-*> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
-*> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
-*> choice of S puts the condition number of B within a factor N of the
-*> smallest possible condition number over all possible diagonal
-*> scalings.
+*> (with respect to the spectral norm). S contains the scale factors,
+*> chosen so that the scaled matrix B with elements
+*> B(i,j) = S(i)*A(i,j)*S(j) has diagonal entries close to one. S(i) is
+*> a power of b nearest to but not exceeding 1/sqrt(A(i,i)), where b is
+*> the basis use for floating point numbers on this machine. This choice
+*> of S avoids round-off errors when computing B.
 *> \endverbatim
 *
 *  Arguments: