HermiteRuleFactory (Apache Commons Math 3.6.1 API)

org.apache.commons.math3.analysis.integration.gauss

## Class HermiteRuleFactory

- java.lang.Object
- - org.apache.commons.math3.analysis.integration.gauss.BaseRuleFactory<Double>
  - - org.apache.commons.math3.analysis.integration.gauss.HermiteRuleFactory

-     public class HermiteRuleFactory
      extends BaseRuleFactory<Double>

  Factory that creates a Gauss-type quadrature rule using Hermite polynomials of the first kind. Such a quadrature rule allows the calculation of improper integrals of a function

  \(f(x) e^{-x^2}\)

  Recurrence relation and weights computation follow Abramowitz and Stegun, 1964.

  The coefficients of the standard Hermite polynomials grow very rapidly. In order to avoid overflows, each Hermite polynomial is normalized with respect to the underlying scalar product. The initial interval for the application of the bisection method is based on the roots of the previous Hermite polynomial (interlacing). Upper and lower bounds of these roots are provided by

  > I. Krasikov, Nonnegative quadratic forms and bounds on orthogonal polynomials, Journal of Approximation theory 111, 31-49

  Since:
    3.3

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `HermiteRuleFactory()`

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `protected Pair<Double[],Double[]>` | `computeRule(int numberOfPoints)` Computes the rule for the given order.

    - ### Methods inherited from class org.apache.commons.math3.analysis.integration.gauss.BaseRuleFactory

      `addRule, getRule, getRuleInternal`

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Constructor Detail

    - #### HermiteRuleFactory

          public HermiteRuleFactory()

  - ### Method Detail

    - #### computeRule

          protected Pair<Double[],Double[]> computeRule(int numberOfPoints)
                                                 throws DimensionMismatchException

      Computes the rule for the given order.
      Specified by:
        `computeRule` in class `BaseRuleFactory<Double>`
      Parameters:
        `numberOfPoints` - Order of the rule to be computed.
      Returns:
        the computed rule.
      Throws:
        `DimensionMismatchException` - if the elements of the pair do not have the same length.

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