Compute new starting approximations to the roots of the polynomial having coefficients of modulus apoly, by means of the Rouche'-based criterion of Bini (Numer. Algo. 1996). More...
This function scans the existing clusters and selects the ones where shift in the gravity center must be done. Then computes the gravity center g, performs the shift of the variable and compute new starting approximations in the cluster (floating point version). More...
This function scans the existing clusters and selects the ones where shift in the gravity center must be done. Then computes the gravity center g, performs the shift of the variable and compute new starting approximations in the cluster (DPE version). More...
This function scans the existing clusters and selects the ones where shift in the gravity center must be done. Then computes the gravity center g, performs the shift of the variable and compute new starting approximations in the cluster (MP version). More...
This routine computes the first coefficients of the shifted polynomial , by performing Horner divisions. This if the floating point version of this function. More...
This routine computes the first coefficients of the shifted polynomial , by performing Horner divisions. This if the DPE version of this function. More...
This routine computes the first coefficients of the shifted polynomial , by performing Horner divisions. This if the MP version of this function. More...
Select appropriate starting point for the approximation of the roots of the given polynomial by applying a divide-and-conquer strategy described in {TODO: Reference missing}. More...
Select appropriate starting point for the approximation of the roots of the given polynomial by applying a divide-and-conquer strategy described in {TODO: Reference missing}. More...
Select appropriate starting point for the approximation of the roots of the given polynomial by applying a divide-and-conquer strategy described in {TODO: Reference missing}. More...
This function scans the existing clusters and selects the ones where shift in the gravity center must be done. Then computes the gravity center g, performs the shift of the variable and compute new starting approximations in the cluster (DPE version).
Shift in g is perfomed if the approximation is included in the search set or its inclusion status has not been determined yet.
To compute g, first compute the weighted mean (super center sc) of the approximations in the cluster, where the weight are the radii, then compute the radius (super radius sr) of the disk centered in the super center containing all the disks of the cluster. Apply few steps of Newton's iteration to the (m-1)-st derivative of the polynomial starting from the super center and obtain the point g where to shift the variable. If g is outside the super disk of center sc and radius sr output a warning message.
Compute new starting approximations to the roots of the polynomial having coefficients of modulus apoly, by means of the Rouche'-based criterion of Bini (Numer. Algo. 1996).
The program can compute all the approximations (if is the degree of ) or it may compute the approximations of the cluster of the cluster_item. The status vector is changed into 'o' for the components that belong to a cluster with relative radius less than eps. The status vector is changed into 'f' for the components that cannot be represented as >dpe.
This function scans the existing clusters and selects the ones where shift in the gravity center must be done. Then computes the gravity center g, performs the shift of the variable and compute new starting approximations in the cluster (floating point version).
Shift in g is perfomed if the approximation is included in the search set or its inclusion status has not been determined yet.
To compute g, first compute the weighted mean (super center sc) of the approximations in the cluster, where the weight are the radii, then compute the radius (super radius sr) of the disk centered in the super center containing all the disks of the cluster. Apply few steps of Newton's iteration to the (m-1)-st derivative of the polynomial starting from the super center and obtain the point g where to shift the variable. If g is outside the super disk of center sc and radius sr output a warning message.
This routine computes the first coefficients of the shifted polynomial , by performing Horner divisions. This if the floating point version of this function.
Compute new starting approximations to the roots of the polynomial having coefficients of modulus apoly.
Computations is done by means of the Rouche'-based criterion of Bini (Numer. Algo. 1996). The program can compute all the approximations (if is the degree of ) or it may compute the approximations of the cluster in the cluster_item. The status vector is changed into 'o' for the components that belong to a cluster with relative radius less than eps. The status vector is changed into 'x' for the components that cannot be represented as double.
Parameters
s
The mps_context associated with the current computation.
n
number of roots in the cluster.
cluster_item
The element of the mps_clusterization of which we are computing the starting points, or NULL if we are computing the starting points for all the approximations.
clust_rad
radius of cluster.
g
gravity center of the cluster.
eps
a double that represent the maximum value of relative radius (with respect to g) of roots whose status must be set to o.
This function scans the existing clusters and selects the ones where shift in the gravity center must be done. Then computes the gravity center g, performs the shift of the variable and compute new starting approximations in the cluster (MP version).
Shift in g is perfomed if the approximation is included in the search set or its inclusion status has not been determined yet.
To compute g, first compute the weighted mean (super center sc) of the approximations in the cluster, where the weight are the radii, then compute the radius (super radius sr) of the disk centered in the super center containing all the disks of the cluster. Apply few steps of Newton's iteration to the (m-1)-st derivative of the polynomial starting from the super center and obtain the point g where to shift the variable. If g is outside the super disk of center sc and radius sr output a warning message.
Select appropriate starting point for the approximation of the roots of the given polynomial by applying a divide-and-conquer strategy described in {TODO: Reference missing}.
Select appropriate starting point for the approximation of the roots of the given polynomial by applying a divide-and-conquer strategy described in {TODO: Reference missing}.
Select appropriate starting point for the approximation of the roots of the given polynomial by applying a divide-and-conquer strategy described in {TODO: Reference missing}.