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On the calculation of elliptic integrals of the second and third kinds

100%

Neuman E.

Applicationes Mathematicae

|

1969-1970

|

tom 11

|

nr 1

91-94

2

Algorithms 70-71. Determination of a quadratic spline function with given values of the integrals in subintervals

100%

Neuman E.

Applicationes Mathematicae

|

1977-1980

|

tom 16

|

nr 4

681-689

3

On the inversion of certain band matrices

100%

Neuman E.

Mathematica Applicanda

|

1977

|

tom 5

|

nr 9

EN

Inversion of band matrices is the simplest, direct way of computing interpolating splines. On the other hand, when studying the convergence problems, the bounds of related inverse matrices are useful. This paper contains algorithms of inversion, based on LR decomposition, of tri- and five-diagonal matrices appearing in spline fitting problems. (In this case LR decomposition is possible and unique if one of the diagonals is fixed.) For example, inversion of a tri-diagonal matrix of dimension n requires 12n(3n+5) multiplications when the proposed algorithm is used. Some upper and lower bounds for elements of the inverse matrix are also given. Under certain additional assumptions the numerical stability is proved. MR0488663

4

Algorithms 52-53. Determination of an interpolating quintic spline function with equally spaced and double knots

100%

Neuman E.

Applicationes Mathematicae

|

1977-1980

|

tom 16

|

nr 1

133-142

5

Algorithm 1. Elliptic integrals of the second and third kinds

100%

Neuman E.

Applicationes Mathematicae

|

1969-1970

|

tom 11

|

nr 1

99-102

6

Optimal quadratures for a certain class of analytic functions

100%

Neuman E.

Applicationes Mathematicae

|

1969-1970

|

tom 11

|

nr 2

173-175

7

Algorithm 30. The calculation of the minimum of a certain function of one variable

88%

Neuman E.

Applicationes Mathematicae

|

1974-1975

|

tom 14

|

nr 1

137-142

8

Algorithm 31. The calculation of the minimum of a certain function of several variables

88%

Neuman E.

Applicationes Mathematicae

|

1974-1975

|

tom 14

|

nr 1

143-164

9

Algorithm 46. Determination of an interpolating quadratic spline function

88%

Neuman E.

Applicationes Mathematicae

|

1976-1977

|

tom 15

|

nr 2

245-250

10

Projections in uniform polynomial approximations

63%

Neuman E.

Applicationes Mathematicae

|

1974-1975

|

tom 14

|

nr 1

99-125

11

On generalized symmetric means and Stirling numbers of the second kind

44%

Neuman E.

Applicationes Mathematicae

|

1983-1985

|

tom 18

|

nr 4

645-656

12

The inversion of cyclic tridiagonal matrices

39%

Łosiak J., Neuman E., Nowak J.

Applicationes Mathematicae

|

1988

|

tom 20

|

nr 1

93-102

Ograniczanie wyników

11 Applicationes Mathematicae

1 Mathematica Applicanda

12 Neuman E.

1 Nowak J.

1 Łosiak J.

1 1988

1 1985

1 1980

2 1977

1 1976

3 1974

1 1970

2 1969

On the calculation of elliptic integrals of the second and third kinds

Algorithms 70-71. Determination of a quadratic spline function with given values of the integrals in subintervals

On the inversion of certain band matrices

Algorithms 52-53. Determination of an interpolating quintic spline function with equally spaced and double knots

Algorithm 1. Elliptic integrals of the second and third kinds

Optimal quadratures for a certain class of analytic functions

Algorithm 30. The calculation of the minimum of a certain function of one variable

Algorithm 31. The calculation of the minimum of a certain function of several variables

Algorithm 46. Determination of an interpolating quadratic spline function

Projections in uniform polynomial approximations

On generalized symmetric means and Stirling numbers of the second kind

The inversion of cyclic tridiagonal matrices