QUADF algorithms are based on the numerical integration package QUADPACK. QUADF default algorithm is QAG. You can override the default algorithm in optional argument 5 with the key ALGOR For example: =QUADF(f, x, a, b, {'algor','qags'}).
- QNG
- A non-adaptive algorithm which uses fixed Gauss-Kronrod-Patterson abscissae to sample the integrand at a maximum of 87 points. It is suitable for fast integration of smooth functions.
- QAG
- An adaptive integration algorithm which divides the integration region into subintervals, and on each iteration the subinterval with the largest estimated error is bisected. This reduces the overall error rapidly, as the subintervals become concentrated around local difficulties in the integrand. The integration rule can be set by the GKPAIR key/value pair.
- QAGS
- Combines QAG with the Wynn epsilon-algorithm to speed up the integration of many types of integrable singularities. It uses 21-point Gauss-Kronrod rule.
- QAGP
- Applies QAGS taking into account user-supplied locations of singular points.
- QAGI
- Used for improper integrals. The integral is mapped onto the semi-open interval (0,1] using the transformation x = (1-t)/t. It is then integrated using the QAGS algorithm using a 15-point Gauss-Kronrod rule
- QKn
- The fixed-order Gauss-Legendre integration routines are provided for fast integration of smooth functions. The n-point Gauss-Legendre rule is exact for polynomials of order 2*n-1 or less. Rules are available for n = 15, 21, 31, 41, 51, 61. (e.g., QK21.)
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A natural cubic spline with continuous second derivative in the interior and zero second derivative at the end points. Integrate from point t1 up to point t2. CubicSplinesIntersection - x value of intersection point between two cubic splines. Jan 20, 2019 Homework 2 — Exponential Integral Function Summer 2001 24 July 2001 — Due Tuesday 31 July 2001 2.2 The Exponential Integral Function — Graphical Presentations 2.2.a Using your functional approximations (from part 2.1.c) and the data in the attached file, you are to estimate the E1(x) function for the range 1x10-5. This article describes the formula syntax and usage of the EXP function in Microsoft Excel. Returns e raised to the power of number. The constant e equals 2.5904, the base of the natural logarithm. EXP(number) The EXP function syntax has the following arguments: Number Required. The exponent applied to the base e.