Selection of starting points and shifting of the polynomials to zoom in the clusters.
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MPS_BEGIN_DECLS void | mps_fstart (mps_context *s, int n, mps_cluster_item *cluster, double clust_rad, double g, rdpe_t eps_out, double fap[]) |
| Compute new starting approximations to the roots of the polynomial having coefficients of modulus apoly. More...
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void | mps_dstart (mps_context *s, int n, mps_cluster_item *cluster, rdpe_t clust_rad, rdpe_t g, rdpe_t eps_out, rdpe_t dap[]) |
| 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...
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void | mps_mstart (mps_context *s, int n, mps_cluster_item *cluster, rdpe_t clust_rad, rdpe_t g, rdpe_t dap[], mpc_t gg) |
| Multiprecision version of mps_fstart() More...
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void | mps_frestart (mps_context *s) |
| 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...
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void | mps_drestart (mps_context *s) |
| 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...
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void | mps_mrestart (mps_context *s) |
| 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...
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void | mps_fshift (mps_context *s, int m, mps_cluster_item *cluster, double clust_rad, cplx_t g, rdpe_t eps) |
| This routine computes the first coefficients of the shifted polynomial , by performing Horner divisions. This if the floating point version of this function. More...
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void | mps_dshift (mps_context *s, int m, mps_cluster_item *cluster, rdpe_t clust_rad, cdpe_t g, rdpe_t eps) |
| This routine computes the first coefficients of the shifted polynomial , by performing Horner divisions. This if the DPE version of this function. More...
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void | mps_mshift (mps_context *s, int m, mps_cluster_item *cluster, rdpe_t clust_rad, mpc_t g) |
| This routine computes the first coefficients of the shifted polynomial , by performing Horner divisions. This if the MP version of this function. More...
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void | mps_recursive_fstart (mps_context *ctx, mps_polynomial *poly, mps_approximation **approximations) |
| 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...
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void | mps_recursive_dstart (mps_context *ctx, mps_polynomial *poly, mps_approximation **approximations) |
| 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...
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void | mps_recursive_mstart (mps_context *ctx, mps_polynomial *poly, mps_approximation **approximations) |
| 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...
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void | mps_file_fstart (mps_context *ctx, mps_polynomial *poly, mps_approximation **approximations) |
| Select the starting points for the polynomial by loading the approximations loaded in the file that has been opened in ctx->rtstr. More...
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void | mps_file_dstart (mps_context *ctx, mps_polynomial *poly, mps_approximation **approximations) |
| Select the starting points for the polynomial by loading the approximations loaded in the file that has been opened in ctx->rtstr. More...
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void | mps_file_mstart (mps_context *ctx, mps_polynomial *poly, mps_approximation **approximations) |
| Select the starting points for the polynomial by loading the approximations loaded in the file that has been opened in ctx->rtstr. More...
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Selection of starting points and shifting of the polynomials to zoom in the clusters.
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).
- Parameters
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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 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).
- Parameters
-
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 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).
- Parameters
-
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.