On the Solution of Linear Equations in Infinitely Many Variables
On the Solution of Linear Equations in Infinitely Many Variables
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If A^O, X^^ ^ is_a solution of (1); the K^ are limited, and this is the only solution for which the. X^ are limit ei.
THEOREM lb. If i^^o , the homogeneous system corresponding to (1) always , has a solution oth e r than the ev ident solution X^^^C . The sy stem (1) itself has_eith er no soluti oiLjin which_case equations (1) are incon si stent ] or has an infinite number ofsolutions. * The use of infinite determinants is by no means the only method of solving equations of type (1). Next I shal...l use a direct method of successive approximations - a method similar to the Picard approximation process which is well known in connection with the theory of differential equations^. So far as I am aware, this method has never been previously applied - in either theory or practice - to solve systems of type (1).® The theory as developed below gives not only a nurcber of new theoreiEs, but also includes THEOREM! la of von Koch. Moreover, the method of successive approximations is not only useful for the theory as developed below; it is a practical method for numerical computation.
What to read after On the Solution of Linear Equations in Infinitely Many Variables?
You can find similar books in the "Read Also" column, or choose other free books by Walsh, J. L. (Joseph Leonard), 1895- to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
If A^O, X^^ ^ is_a solution of (1); the K^ are limited, and this is the only solution for which the. X^ are limit ei.
THEOREM lb. If i^^o , the homogeneous system corresponding to (1) always , has a solution oth e r than the ev ident solution X^^^C . The sy stem (1) itself has_eith er no soluti oiLjin which_case equations (1) are incon si stent ] or has an infinite number ofsolutions. * The use of infinite determinants is by no means the only method of solving equations of type (1). Next I shal...l use a direct method of successive approximations - a method similar to the Picard approximation process which is well known in connection with the theory of differential equations^. So far as I am aware, this method has never been previously applied - in either theory or practice - to solve systems of type (1).® The theory as developed below gives not only a nurcber of new theoreiEs, but also includes THEOREM! la of von Koch. Moreover, the method of successive approximations is not only useful for the theory as developed below; it is a practical method for numerical computation.
What to read after On the Solution of Linear Equations in Infinitely Many Variables?
You can find similar books in the "Read Also" column, or choose other free books by Walsh, J. L. (Joseph Leonard), 1895- to read onlineMoreLess
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