Operational equations for data in rectangular array

Silver, G. L.

doi:10.1016/s0167-9473(98)00029-2

Cited by 12 publications

(7 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…See Eq. (7) in [1] and the discussion following that equation. This observation implies the preceding methods are potentially more fertile than methods that are based on applied operational calculus [2,3].…”

Section: Discussionmentioning

confidence: 98%

“…1. The coordinates of vertices A, B, C, and D are (-1,-1), (1,-1), (-1,1), and (1,1) respectively. The distance between any vertex and its two nearest neighbors is two units.…”

Section: A Cubic Equation For Four Positive Numbers In a Rectangular mentioning

confidence: 99%

“…Several years ago, a new equation appeared for the interpolation of four positive, bilinear numbers in rectangular array. The new equation is also exact on the squares of the original bilinear numbers [1].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Equations for the four-point rectangle

Silver¹

2019

ams

View full text Add to dashboard Cite

Four numbers in a rectangular array can be interpolated by the bilinear equation. If the numbers are positive, they can be interpolated by a new bi-cubic equation. The array can be interpolated by eight new fourth-degree equations. The positive squareroots of the fourth-degree equations are new bi-quadratic equations that are applicable to the analysis of the same four-point arrays. The new equations are suitable for the analysis of two-parameter laboratory experiments. Mathematics Subject Classification: 65D05, 65D07, 65D17

show abstract

Section: Discussionmentioning

confidence: 98%

“…1. The coordinates of vertices A, B, C, and D are (-1,-1), (1,-1), (-1,1), and (1,1) respectively. The distance between any vertex and its two nearest neighbors is two units.…”

Section: A Cubic Equation For Four Positive Numbers In a Rectangular mentioning

confidence: 99%

See 1 more Smart Citation

Equations for the four-point rectangle

Silver¹

2019

ams

View full text Add to dashboard Cite

show abstract

“…Operational methods [2] permit the developments of many unexpected results. The representations of four-and five-point rectangles, and eight-and nine-point rectangular prisms by quadratic, cubic, exponential, and trigonometric equations are among the developments [1][2][3][4][5]. Eq.…”

Section: Y3c:=-1/24*(-c^2+a^2-g^2+i^2)*(a^2+c^2-g^2-i^2)*(a^3-c^3 -G^mentioning

confidence: 99%

“…The bilinear equation is the standard method for interpolating surfaces described by four data in a rectangular array. A quadratic equation for this design was illus-trated several years ago [1]. It was first derived by operational methods [2].…”

Section: Introductionmentioning

confidence: 99%