.. _method-polynomial_chaos-expansion_order-collocation_ratio-least_squares:

"""""""""""""
least_squares
"""""""""""""


Compute the coefficients of a polynomial expansion using least squares


.. toctree::
   :hidden:
   :maxdepth: 1

   method-polynomial_chaos-expansion_order-collocation_ratio-least_squares-svd
   method-polynomial_chaos-expansion_order-collocation_ratio-least_squares-equality_constrained


**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* svd


**Child Keywords:**

+-------------------------+--------------------+--------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword           | Dakota Keyword Description                    |
|                         | Group              |                          |                                               |
+=========================+====================+==========================+===============================================+
| Optional (Choose One)   | LSQ Regression     | `svd`__                  | Calculate the coefficients of a polynomial    |
|                         | Approach           |                          | chaos expansion using the singular value      |
|                         |                    |                          | decomposition.                                |
|                         |                    +--------------------------+-----------------------------------------------+
|                         |                    | `equality_constrained`__ | Calculate the coefficients of a polynomial    |
|                         |                    |                          | chaos expansion using equality constrained    |
|                         |                    |                          | least squares.                                |
+-------------------------+--------------------+--------------------------+-----------------------------------------------+

.. __: method-polynomial_chaos-expansion_order-collocation_ratio-least_squares-svd.html
__ method-polynomial_chaos-expansion_order-collocation_ratio-least_squares-equality_constrained.html



**Description**


Compute the coefficients of a polynomial expansion using least squares. Specifically SVD-based least-squares will be used for solving over-determined systems. For the situation when the number of function values is smaller than the number of terms in a PCE, but the total number of samples including gradient values is greater than the number of terms, the resulting over-determined system will be solved using equality constrained least squares


