P. H. Leslie. 1945. - Historial de revisiones

Lcgarcia en 04:00 17 abr 2021

2021-04-17T04:00:44Z

← Revisión anterior		Revisión del 06:00 17 abr 2021
Línea 1:		Línea 1:
	'''P. H. Leslie. 1945. On the Use of Matrices in Certain Population Mathematics. Biometrika 33(3): 183-212. Oxford University Press.'''		'''P. H. Leslie. 1945. On the Use of Matrices in Certain Population Mathematics. Biometrika 33(3): 183-212. Oxford University Press.''' [[Archivo:PH Leslie 1945 Matrices in Population Mathematics.pdf]]. 3,53 MB

	''Leslie's work, rather than that of his predecessors Bernardelli and Lewis, is most commonly cited in the widespread literature using matrices, largely for the reason that Leslie worked out the mathematics and the application with great thoroughness. Some of his elaboration was designed to save arithmetic-for example his transformation of the projection matrix into an equivalent form with unity in the subdiagonal positions. Such devices, like a considerable part of classical numerical analysis, are unnecessary in a computer era.''		''Leslie's work, rather than that of his predecessors Bernardelli and Lewis, is most commonly cited in the widespread literature using matrices, largely for the reason that Leslie worked out the mathematics and the application with great thoroughness. Some of his elaboration was designed to save arithmetic-for example his transformation of the projection matrix into an equivalent form with unity in the subdiagonal positions. Such devices, like a considerable part of classical numerical analysis, are unnecessary in a computer era.''

Lcgarcia en 03:54 17 abr 2021

2021-04-17T03:54:33Z

← Revisión anterior		Revisión del 05:54 17 abr 2021
Línea 5:		Línea 5:
	''The case of double roots seemed to require attention, for Leslie could not then know that no case of double roots would ever arise with real data. In the present excerpt we omit this, as well as the spectral decomposition of the matrix, which has not found extensive application.''		''The case of double roots seemed to require attention, for Leslie could not then know that no case of double roots would ever arise with real data. In the present excerpt we omit this, as well as the spectral decomposition of the matrix, which has not found extensive application.''

	''Among the latent roots or eigen values and the corresponding stable vectors, as Leslie points out, demographic and biological interest is confined to three. The first, of largest absolute value, is positive and represents the ratio of population at the end of a cycle to that at the beginning, when the process has been operating for a considerable period; it provides the component of geometric increase. The second and third roots produce waves of diminishing amplitude having the length of the generation, usually 25 to 30 years. These waves measure the echo effect-after a baby boom they provide for a smaller boom a generation later-on the condition that the age·specific rates of birth and death remain constant.		''Among the latent roots or eigen values and the corresponding stable vectors, as Leslie points out, demographic and biological interest is confined to three. The first, of largest absolute value, is positive and represents the ratio of population at the end of a cycle to that at the beginning, when the process has been operating for a considerable period; it provides the component of geometric increase. The second and third roots produce waves of diminishing amplitude having the length of the generation, usually 25 to 30 years. These waves measure the echo effect-after a baby boom they provide for a smaller boom a generation later-on the condition that the age·specific rates of birth and death remain constant.<be>
	D. P. Smith et al., Mathematical Demography''~~<br>~~		:D. P. Smith et al., Mathematical Demography''
	© Springer-Verlag Berlin · Heidelberg 1977		:© Springer-Verlag Berlin · Heidelberg 1977
	----		----
	# Introduction 183		# Introduction 183

Lcgarcia en 03:53 17 abr 2021

2021-04-17T03:53:21Z

← Revisión anterior		Revisión del 05:53 17 abr 2021
Línea 1:		Línea 1:
	'''P. H. Leslie. 1945. On the Use of Matrices in Certain Population Mathematics. Biometrika 33(3): 183-212. Oxford University Press.'''		'''P. H. Leslie. 1945. On the Use of Matrices in Certain Population Mathematics. Biometrika 33(3): 183-212. Oxford University Press.'''

	Leslie's work, rather than that of his predecessors Bernardelli and Lewis, is most commonly cited in the widespread literature using matrices, largely for the reason that Leslie worked out the mathematics and the application with great thoroughness. Some of his elaboration was designed to save arithmetic-for example his transformation of the projection matrix into an equivalent form with unity in the subdiagonal positions. Such devices, like a considerable part of classical numerical analysis, are unnecessary in a computer era.		''Leslie's work, rather than that of his predecessors Bernardelli and Lewis, is most commonly cited in the widespread literature using matrices, largely for the reason that Leslie worked out the mathematics and the application with great thoroughness. Some of his elaboration was designed to save arithmetic-for example his transformation of the projection matrix into an equivalent form with unity in the subdiagonal positions. Such devices, like a considerable part of classical numerical analysis, are unnecessary in a computer era.''

	The case of double roots seemed to require attention, for Leslie could not then know that no case of double roots would ever arise with real data. In the present excerpt we omit this, as well as the spectral decomposition of the matrix, which has not found extensive application.		''The case of double roots seemed to require attention, for Leslie could not then know that no case of double roots would ever arise with real data. In the present excerpt we omit this, as well as the spectral decomposition of the matrix, which has not found extensive application.''

	Among the latent roots or eigen values and the corresponding stable vectors, as Leslie points out, demographic and biological interest is confined to three. The first, of largest absolute value, is positive and represents the ratio of population at the end of a cycle to that at the beginning, when the process has been operating for a considerable period; it provides the component of geometric increase. The second and third roots produce waves of diminishing amplitude having the length of the generation, usually 25 to 30 years. These waves measure the echo effect-after a baby boom they provide for a smaller boom a generation later-on the condition that the age·specific rates of birth and death remain constant.		''Among the latent roots or eigen values and the corresponding stable vectors, as Leslie points out, demographic and biological interest is confined to three. The first, of largest absolute value, is positive and represents the ratio of population at the end of a cycle to that at the beginning, when the process has been operating for a considerable period; it provides the component of geometric increase. The second and third roots produce waves of diminishing amplitude having the length of the generation, usually 25 to 30 years. These waves measure the echo effect-after a baby boom they provide for a smaller boom a generation later-on the condition that the age·specific rates of birth and death remain constant.
	D. P. Smith et al., Mathematical Demography<br>		D. P. Smith et al., Mathematical Demography''<br>
	© Springer-Verlag Berlin · Heidelberg 1977		© Springer-Verlag Berlin · Heidelberg 1977
			----
	#. Introduction 183		# Introduction 183
	#. Derivation of the matrix elements 184		# Derivation of the matrix elements 184
	#. Numerical example 185		# Numerical example 185
	#. Properties of the basic matrix 187		# Properties of the basic matrix 187
	#. Transformation of the co-ordinate system 188		# Transformation of the co-ordinate system 188
	#. Relation between the canonical1		# Relation between the canonical1
	#. Properties of the stable vectors . 193		# Properties of the stable vectors . 193
	#. The spectral set of operators 194		# The spectral set of operators 194
	#. Reduction of B to classical canonical form 195		# Reduction of B to classical canonical form 195
	#. The relation between rp and l/r vectors 197		# The relation between rp and l/r vectors 197
	#. Case of repeated latent roots 198		# Case of repeated latent roots 198
	#. The approach to the stable age distribution 199		# The approach to the stable age distribution 199
	#. Special case of the matrix with only a single non-zero F. element 200		# Special case of the matrix with only a single non-zero F. element 200
	#. Numerical comparison with the usual methods of computation 201		# Numerical comparison with the usual methods of computation 201
	#. Further practical applications 207		# Further practical applications 207
	Appendix:		Appendix:
	::(1) The tables of mortality and fertility 209		::(1) The tables of mortality and fertility 209

Lcgarcia: nueva referencia

2021-04-17T03:49:32Z

nueva referencia

@@ Línea 1: / Línea 1: @@
-P. H. Leslie. 1945. On the Use of Matrices in Certain Population Mathematics. Biometrika 33(3): 183-212. Oxford University Press.
+'''P. H. Leslie. 1945. On the Use of Matrices in Certain Population Mathematics. Biometrika 33(3): 183-212. Oxford University Press.'''
 Leslie's work, rather than that of his predecessors Bernardelli and Lewis, is most commonly cited in the widespread literature using matrices, largely for the reason that Leslie worked out the mathematics and the application with great thoroughness. Some of his elaboration was designed to save arithmetic-for example his transformation of the projection matrix into an equivalent form with unity in the subdiagonal positions. Such devices, like a considerable part of classical numerical analysis, are unnecessary in a computer era.
@@ Línea 5: / Línea 5: @@
 The case of double roots seemed to require attention, for Leslie could not then know that no case of double roots would ever arise with real data. In the present excerpt we omit this, as well as the spectral decomposition of the matrix, which has not found extensive application.
-Among the latent roots or eigen values and the corresponding stable vectors, as Leslie points out, demographic and biological interest is confined to three. The first, of largest absolute value, is positive and represents the ratio of population at the end of a cycle to that at the beginning, when the process has been operating for a considerable period; it provides the component of geometric
+Among the latent roots or eigen values and the corresponding stable vectors, as Leslie points out, demographic and biological interest is confined to three. The first, of largest absolute value, is positive and represents the ratio of population at the end of a cycle to that at the beginning, when the process has been operating for a considerable period; it provides the component of geometric increase. The second and third roots produce waves of diminishing amplitude having the length of the generation, usually 25 to 30 years. These waves measure the echo effect-after a baby boom they provide for a smaller boom a generation later-on the condition that the age·specific rates of birth and death remain constant.
-increase. The second and third roots produce waves of diminishing amplitude having the length of the generation, usually 25 to 30 years. These waves measure the echo effect-after a baby boom they provide for a smaller boom a generation later-on the condition that the age·specific rates of birth and death remain constant.
+D. P. Smith et al., Mathematical Demography<br>
 © Springer-Verlag Berlin · Heidelberg 1977

Lcgarcia: nueva referencia

2021-04-17T03:29:57Z

nueva referencia

Página nueva

P. H. Leslie. 1945. On the Use of Matrices in Certain Population Mathematics. Biometrika 33(3): 183-212. Oxford University Press.

Leslie's work, rather than that of his predecessors Bernardelli and Lewis, is most commonly cited in the widespread literature using matrices, largely for the reason that Leslie worked out the mathematics and the application with great thoroughness. Some of his elaboration was designed to save arithmetic-for example his transformation of the projection matrix into an equivalent form with unity in the subdiagonal positions. Such devices, like a considerable part of classical numerical analysis, are unnecessary in a computer era.

The case of double roots seemed to require attention, for Leslie could not then know that no case of double roots would ever arise with real data. In the present excerpt we omit this, as well as the spectral decomposition of the matrix, which has not found extensive application.

Among the latent roots or eigen values and the corresponding stable vectors, as Leslie points out, demographic and biological interest is confined to three. The first, of largest absolute value, is positive and represents the ratio of population at the end of a cycle to that at the beginning, when the process has been operating for a considerable period; it provides the component of geometric
increase. The second and third roots produce waves of diminishing amplitude having the length of the generation, usually 25 to 30 years. These waves measure the echo effect-after a baby boom they provide for a smaller boom a generation later-on the condition that the age·specific rates of birth and death remain constant.
D. P. Smith et al., Mathematical Demography
© Springer-Verlag Berlin · Heidelberg 1977